Analytical Solvers


Numbering the entered equations:
X1 +X2 +4X3 -12X4 -2X5 = 17   ... 1 
X1 +72X2 +X3 +2X4 -2X5 = -3   ... 2+ Show More
Simplifying,
⇒ X1 + 32X2 - X3 + 2X2 + 2X4 - 2X5 = - 3 - 4X3 + 2X3
⇒ X1 + 72X2 - X3 + 2X4 - 2X5 = - 3 - 2X3+ Show More
L.H.S.
= X1 + 32X2 - X3 + 2X2 + 2X4 - 2X5
= X1 + 72X2 - X3 + 2X4 - 2X5+ Show More
32X2 + 2X2
= [32 + 2]X2
= 72X2 + Show More
32 + 2
= 3×1 + 2×22
= 3+42
= 72

R.H.S.
= - 3 - 4X3 + 2X3
= - 3 - 2X3+ Show More
(-4)X3 + 2X3
= [(-4) + 2]X3
= -2X3 + Show More
-4 + 2
= -2

Subtracting same quantity from both sides of the above equation,
⇒ [X1 + 72X2 - X3 + 2X4 - 2X5] - [- 2X3] = [- 3 - 2X3] - [- 2X3]
⇒ X1 + 72X2 + X3 + 2X4 - 2X5 = - 3+ Show More
L.H.S.
= X1 + 72X2 - X3 + 2X4 - 2X5 + 2X3
= X1 + 72X2 + X3 + 2X4 - 2X5+ Show More
(-1)X3 + 2X3
= [(-1) + 2]X3
= 1X3 + Show More
-1 + 2
= 1

R.H.S.
= - 3 - 2X3 + 2X3
= - 3 + 0+ Show More
(-2)X3 + 2X3
= [(-2) + 2]X3
= 0X3 + Show More
-2 + 2
= 0
52X1 +32X2 +3X3     = 854   ... 3 
2X1 -32X2 +3X3     = 252   ... 4 
5X1 -X2 +2X3     = 2   ... 5 

Reorganizing the system:
52X1 +32X2 +3X3     = 854   ... 6 Same as 3
2X1 -32X2 +3X3     = 252   ... 7 Same as 4
5X1 -X2 +2X3     = 2   ... 8 Same as 5
X1 +72X2 +X3 +2X4 -2X5 = -3   ... 9 Same as 2
X1 +X2 +4X3 -12X4 -2X5 = 17   ... 10 Same as 1

Eliminating variable X1 from equation 6 and 7
- 274X2 + 32X3 = - 454   ... 11+ Show More
We have,
52X1 +32X2 +3X3 = 854
2X1 -32X2 +3X3 = 252


Multiplying the first and second equations by -2 and 52 respectively we get,

-5X1 -3X2 -6X3 = -852+ Show More
L.H.S.
= [52X1 + 32X2 + 3X3]×-2
= [52X1×-2] + [32X2×-2] + [3X3×-2]
= - 5X1 - 3X2 - 6X3 + Show More
Simplification 1:
52X1×(-2)
= [52×(-2)]X1
= -5X1 + Show More
52×(-2)
= 51×2×-1×21
= 51×2×-1×21
= 51×-11
= -5

Simplification 2:
32X2×(-2)
= [32×(-2)]X2
= -3X2 + Show More
32×(-2)
= 31×2×-1×21
= 31×2×-1×21
= 31×-11
= -3

Simplification 3:
3X3×(-2)
= [3×(-2)]X3
= -6X3 + Show More
3×(-2)
= -6



R.H.S.
= [854]×-2
= [854×-2]
= - 852 + Show More
854×(-2)
= -852 + Show More
854×(-2)
= 852×2×-1×21
= 852×2×-1×21
= 852×-11
= -852
5X1 -154X2 +152X3 = 1254+ Show More
L.H.S.
= [2X1 - 32X2 + 3X3]×52
= [2X1×52] + [-32X2×52] + [3X3×52]
= 5X1 - 154X2 + 152X3 + Show More
Simplification 1:
2X1×52
= [2×52]X1
= 5X1 + Show More
2×52
= 1×21×51×2
= 1×21×51×2
= 11×51
= 5

Simplification 2:
-32X2×52
= [-32×52]X2
= -154X2 + Show More
-32×52
= (-3)×52×2
= -154

Simplification 3:
3X3×52
= [3×52]X3
= 152X3 + Show More
3×52
= 3×51×2
= 152



R.H.S.
= [252]×52
= [252×52]
= 1254 + Show More
252×52
= 1254 + Show More
252×52
= 25×52×2
= 1254


Adding these two equations we get,

 -5X1 -3X2 -6X3 = -852 
(+)5X1 -154X2 +152X3 = 1254 
   -274X2 +32X3 = -454+ Show More
L.H.S.
= [- 5X1 - 3X2 - 6X3] + [5X1 - 154X2 + 152X3]
= - 5X1 - 3X2 - 6X3 + 5X1 - 154X2 + 152X3
= - 5X1 + 5X1 - 3X2 - 154X2 - 6X3 + 152X3
= 0 - 274X2 + 32X3+ Show More
Simplification 1:
(-5)X1 + 5X1
= [(-5) + 5]X1
= 0X1 + Show More
-5 + 5
= 0

Simplification 2:
(-3)X2 + -154X2
= [(-3) + -154]X2
= -274X2 + Show More
-3 + -154
= (-3)×4 + (-15)×14
= (-12)+(-15)4
= -274

Simplification 3:
(-6)X3 + 152X3
= [(-6) + 152]X3
= 32X3 + Show More
-6 + 152
= (-6)×2 + 15×12
= (-12)+152
= 32


= - 274X2 + 32X3

R.H.S.
= [- 852] + [1254]
= - 852 + 1254
= - 454+ Show More
-852 + 1254
= -454 + Show More
-852 + 1254
= (-85)×4 + 125×22×4
= (-340)+2508
= -908
= -454×22
= -454×1
= -454
Eliminating variable X1 from equation 7 and 8
112X2 - 11X3 = - 1172   ... 12+ Show More
We have,
2X1 -32X2 +3X3 = 252
5X1 -X2 +2X3 = 2


Multiplying the first and second equations by -5 and 2 respectively we get,

-10X1 +152X2 -15X3 = -1252+ Show More
L.H.S.
= [2X1 - 32X2 + 3X3]×-5
= [2X1×-5] + [-32X2×-5] + [3X3×-5]
= - 10X1 + 152X2 - 15X3 + Show More
Simplification 1:
2X1×(-5)
= [2×(-5)]X1
= -10X1 + Show More
2×(-5)
= -10

Simplification 2:
-32X2×(-5)
= [-32×(-5)]X2
= 152X2 + Show More
-32×(-5)
= (-3)×(-5)2×1
= 152

Simplification 3:
3X3×(-5)
= [3×(-5)]X3
= -15X3 + Show More
3×(-5)
= -15



R.H.S.
= [252]×-5
= [252×-5]
= - 1252 + Show More
252×(-5)
= -1252 + Show More
252×(-5)
= 25×(-5)2×1
= -1252
10X1 -2X2 +4X3 = 4+ Show More
L.H.S.
= [5X1 - X2 + 2X3]×2
= [5X1×2] + [-X2×2] + [2X3×2]
= 10X1 - 2X2 + 4X3 + Show More
Simplification 1:
5X1×2
= [5×2]X1
= 10X1 + Show More
5×2
= 10

Simplification 2:
(-1)X2×2
= [(-1)×2]X2
= -2X2 + Show More
(-1)×2
= -2

Simplification 3:
2X3×2
= [2×2]X3
= 4X3 + Show More
2×2
= 4



R.H.S.
= [2]×2
= [2×2]
= 4 + Show More
2×2
= 4 + Show More
2×2
= 4


Adding these two equations we get,

 -10X1 +152X2 -15X3 = -1252 
(+)10X1 -2X2 +4X3 = 4 
   +112X2 -11X3 = -1172+ Show More
L.H.S.
= [- 10X1 + 152X2 - 15X3] + [10X1 - 2X2 + 4X3]
= - 10X1 + 152X2 - 15X3 + 10X1 - 2X2 + 4X3
= - 10X1 + 10X1 + 152X2 - 2X2 - 15X3 + 4X3
= 0 + 112X2 - 11X3+ Show More
Simplification 1:
(-10)X1 + 10X1
= [(-10) + 10]X1
= 0X1 + Show More
-10 + 10
= 0

Simplification 2:
152X2 + (-2)X2
= [152 + (-2)]X2
= 112X2 + Show More
152 + -2
= 15×1 + (-2)×22
= 15+(-4)2
= 112

Simplification 3:
(-15)X3 + 4X3
= [(-15) + 4]X3
= -11X3 + Show More
-15 + 4
= -11


= 112X2 - 11X3

R.H.S.
= [- 1252] + [4]
= - 1252 + 4
= - 1172+ Show More
-1252 + 4
= -1172 + Show More
-1252 + 4
= (-125)×1 + 4×22
= (-125)+82
= -1172

Eliminating variable X2 from equation 11 and 12
66X3 = 18274   ... 13+ Show More
We have,
-274X2 +32X3 = -454
112X2 -11X3 = -1172


Multiplying the first and second equations by -112 and -274 respectively we get,

2978X2 -334X3 = 4958+ Show More
L.H.S.
= [- 274X2 + 32X3]×-112
= [-274X2×-112] + [32X3×-112]
= 2978X2 - 334X3 + Show More
Simplification 1:
-274X2×-112
= [-274×-112]X2
= 2978X2 + Show More
-274×-112
= (-27)×(-11)4×2
= 2978

Simplification 2:
32X3×-112
= [32×-112]X3
= -334X3 + Show More
32×-112
= 3×(-11)2×2
= -334



R.H.S.
= [- 454]×-112
= [-454×-112]
= 4958 + Show More
-454×-112
= 4958 + Show More
-454×-112
= (-45)×(-11)4×2
= 4958
-2978X2 +2974X3 = 31598+ Show More
L.H.S.
= [112X2 - 11X3]×-274
= [112X2×-274] + [-11X3×-274]
= - 2978X2 + 2974X3 + Show More
Simplification 1:
112X2×-274
= [112×-274]X2
= -2978X2 + Show More
112×-274
= 11×(-27)2×4
= -2978

Simplification 2:
(-11)X3×-274
= [(-11)×-274]X3
= 2974X3 + Show More
(-11)×-274
= (-11)×(-27)1×4
= 2974



R.H.S.
= [- 1172]×-274
= [-1172×-274]
= 31598 + Show More
-1172×-274
= 31598 + Show More
-1172×-274
= (-117)×(-27)2×4
= 31598


Adding these two equations we get,

 2978X2 -334X3 = 4958 
(+)-2978X2 +2974X3 = 31598 
   +66X3 = 18274+ Show More
L.H.S.
= [2978X2 - 334X3] + [- 2978X2 + 2974X3]
= 2978X2 - 334X3 - 2978X2 + 2974X3
= 2978X2 - 2978X2 - 334X3 + 2974X3
= 0 + 66X3+ Show More
Simplification 1:
2978X2 + -2978X2
= [2978 + -2978]X2
= 0X2 + Show More
2978 + -2978
= 297 + (-297)8
= 08
= 0

Simplification 2:
-334X3 + 2974X3
= [-334 + 2974]X3
= 66X3 + Show More
-334 + 2974
= (-33) + 2974
= 2644
= 66×44
= 66×1
= 66


= 66X3

R.H.S.
= [4958] + [31598]
= 4958 + 31598
= 18274+ Show More
4958 + 31598
= 18274 + Show More
4958 + 31598
= 495 + 31598
= 36548
= 18274×22
= 18274×1
= 18274

Solving equation 13 for variable X3 we get,
X3 = 60988  Ans.    ... 14+ Show More
66X3 = 18274
Dividing both sides of the above equation by same number,
⇒ [66X3] ÷ [66] = [18274] ÷ [66]
⇒ X3 = 60988+ Show More
L.H.S.
= [66X3]÷66
= [66X3÷66]
= X3 + Show More
66X3÷66
= [66÷66]X3
= 1X3 + Show More
66 ÷ 66
= 66×166
= 1×661×11×66
= 1×661×11×66
= 11×11
= 1


R.H.S.
= [18274]÷66
= [18274÷66]
= 60988 + Show More
18274÷66
= 60988 + Show More
18274 ÷ 66
= 18274×166
= 609×34×122×3
= 609×34×122×3
= 6094×122
= 60988
Substituting the value of variable X3 from equation 14 into 11 we get,
X2 = 14144  Ans.    ... 15+ Show More
Substituting the following equation,
X3 = 60988
into
- 274X2 + 32X3 = - 454
we have,
⇒  - 274X2 + 32×[60988] =  - 454
⇒ - 274X2 + 1827176 = - 454+ Show More
L.H.S.
=  - 274X2 + 32×[60988]
= - 274X2 + [32×60988]
= - 274X2 + 1827176+ Show More
60988×32
= 1827176 + Show More
60988×32
= 609×388×2
= 1827176


R.H.S.
=  - 454

Subtracting same quantity from both sides of the above equation,
⇒ [- 274X2 + 1827176] - [1827176] = [- 454] - [1827176]
⇒ - 274X2 = - 3807176+ Show More
L.H.S.
= - 274X2 + 1827176 - 1827176
= - 274X2 + 0+ Show More
1827176 + -1827176
= 0 + Show More
1827176 + -1827176
= 1827 + (-1827)176
= 0176
= 0

R.H.S.
= - 454 - 1827176
= - 3807176+ Show More
-454 + -1827176
= -3807176 + Show More
-454 + -1827176
= (-45)×176 + (-1827)×44×176
= (-7920)+(-7308)704
= -15228704
= -3807176×44
= -3807176×1
= -3807176

Dividing both sides of the above equation by same number,
⇒ [- 274X2] ÷ [- 274] = [- 3807176] ÷ [- 274]
⇒ X2 = 14144+ Show More
L.H.S.
= [- 274X2]÷-274
= [-274X2÷-274]
= X2 + Show More
-274X2÷-274
= [-274÷-274]X2
= 1X2 + Show More
-274 ÷ -274
= -274×4-27
= 1×-271×4×1×41×-27
= 1×-271×4×1×41×-27
= 11×11
= 1


R.H.S.
= [- 3807176]÷-274
= [-3807176÷-274]
= 14144 + Show More
-3807176÷-274
= 14144 + Show More
-3807176 ÷ -274
= -3807176×4-27
= 141×-2744×4×1×41×-27
= 141×-2744×4×1×41×-27
= 14144×11
= 14144
Substituting the value of variables X3 and X2 from equations 14 and 15 into 6 we get,
X1 = - 1911  Ans.    ... 16+ Show More
Substituting the following equations,
X3 = 60988
X2 = 14144
into
52X1 + 32X2 + 3X3 = 854
we have,
⇒ 52X1 + 32×[14144] + 3×[60988] = 854
⇒ 52X1 + 112544 = 854+ Show More
L.H.S.
= 52X1 + 32×[14144] + 3×[60988]
= 52X1 + [32×14144] + [3×60988]
= 52X1 + 42388 + 182788+ Show More
Simplification 1:
14144×32
= 42388 + Show More
14144×32
= 141×344×2
= 42388

Simplification 2:
60988×3
= 182788 + Show More
14144×32
= 141×344×2
= 42388


= 52X1 + 112544+ Show More
42388 + 182788
= 112544 + Show More
42388 + 182788
= 423 + 182788
= 225088
= 112544×22
= 112544×1
= 112544


R.H.S.
= 854

Subtracting same quantity from both sides of the above equation,
⇒ [52X1 + 112544] - [112544] = [854] - [112544]
⇒ 52X1 = - 9522+ Show More
L.H.S.
= 52X1 + 112544 - 112544
= 52X1 + 0+ Show More
112544 + -112544
= 0 + Show More
112544 + -112544
= 1125 + (-1125)44
= 044
= 0

R.H.S.
= 854 - 112544
= - 9522+ Show More
854 + -112544
= -9522 + Show More
854 + -112544
= 85×44 + (-1125)×44×44
= 3740+(-4500)176
= -760176
= -9522×88
= -9522×1
= -9522

Dividing both sides of the above equation by same number,
⇒ [52X1] ÷ [52] = [- 9522] ÷ [52]
⇒ X1 = - 1911+ Show More
L.H.S.
= [52X1]÷52
= [52X1÷52]
= X1 + Show More
52X1÷52
= [52÷52]X1
= 1X1 + Show More
52 ÷ 52
= 52×25
= 1×51×2×1×21×5
= 1×51×2×1×21×5
= 11×11
= 1


R.H.S.
= [- 9522]÷52
= [-9522÷52]
= - 1911 + Show More
-9522÷52
= -1911 + Show More
-9522 ÷ 52
= -9522×25
= -19×511×2×1×21×5
= -19×511×2×1×21×5
= -1911×11
= -1911

Substituting the value of variables X3, X2 and X1 from equations 14, 15 and 16 into 9 and 10 we get,
-2X4 +2X5 = 42722   ... 17+ Show More
Substituting the following equations,
X3 = 60988
X2 = 14144
X1 = - 1911
into
X1 + 72X2 + X3 + 2X4 - 2X5 = - 3
we have,
⇒ 1×[- 1911] + 72×[14144] + 1×[60988] + 2X4 - 2X5 =  - 3
⇒ 144488 + 2X4 - 2X5 = - 3+ Show More
L.H.S.
= 1×[- 1911] + 72×[14144] + 1×[60988] + 2X4 - 2X5
= [1×-1911] + [72×14144] + [1×60988] + 2X4 - 2X5
= - 1911 + 98788 + 60988 + 2X4 - 2X5+ Show More
Simplification 1:
-1911×1
= -1911 + Show More
-1911×1
= (-19)×111×1
= -1911

Simplification 2:
14144×72
= 98788 + Show More
-1911×1
= (-19)×111×1
= -1911

Simplification 3:
60988×1
= 60988 + Show More
-1911×1
= (-19)×111×1
= -1911


= 144488 + 2X4 - 2X5+ Show More
-1911+98788+60988
= 144488 + Show More
-1911 + 98788 + 60988
= (-19)×8 + 987×1 + 609×188
= (-152)+987+60988
= 144488
= 36122×44
= 36122×1
= 36122


R.H.S.
=  - 3

Subtracting same quantity from both sides of the above equation,
⇒ [144488 + 2X4 - 2X5] - [144488] = [- 3] - [144488]
⇒ 2X4 - 2X5 = - 42722+ Show More
L.H.S.
= 144488 + 2X4 - 2X5 - 144488
= 0 + 2X4 - 2X5+ Show More
144488 + -144488
= 0 + Show More
144488 + -144488
= 1444 + (-1444)88
= 088
= 0

R.H.S.
= - 3 - 144488
= - 42722+ Show More
(-3) + -144488
= -42722 + Show More
-3 + -144488
= (-3)×88 + (-1444)×188
= (-264)+(-1444)88
= -170888
= -42722×44
= -42722×1
= -42722

Dividing both sides of the above equation by same number,
⇒ [2X4 - 2X5] ÷ [- 1] = [- 42722] ÷ [- 1]
⇒ - 2X4 + 2X5 = 42722+ Show More
L.H.S.
= [2X4 - 2X5]÷-1
= [2X4÷-1] + [-2X5÷-1]
= - 2X4 + 2X5 + Show More
Simplification 1:
2X4÷(-1)
= [2÷(-1)]X4
= -2X4 + Show More
2 ÷ (-1)
= 2×1-1
= -2×-1-1
= -2×1
= -2

Simplification 2:
(-2)X5÷(-1)
= [(-2)÷(-1)]X5
= 2X5 + Show More
(-2) ÷ (-1)
= (-2)×1-1
= 2×-1-1
= 2×1
= 2



R.H.S.
= [- 42722]÷-1
= [-42722÷-1]
= 42722 + Show More
-42722÷(-1)
= 42722 + Show More
-42722 ÷ (-1)
= -42722×1-1
= 42722×-1-1
= 42722×1
= 42722
12X4 +2X5 = 53544   ... 18+ Show More
Substituting the following equations,
X3 = 60988
X2 = 14144
X1 = - 1911
into
X1 + X2 + 4X3 - 12X4 - 2X5 = 17
we have,
⇒ 1×[- 1911] + 1×[14144] + 4×[60988] - 12X4 - 2X5 = 17
⇒ 128344 - 12X4 - 2X5 = 17+ Show More
L.H.S.
= 1×[- 1911] + 1×[14144] + 4×[60988] - 12X4 - 2X5
= [1×-1911] + [1×14144] + [4×60988] - 12X4 - 2X5
= - 1911 + 14144 + 60922 - 12X4 - 2X5+ Show More
Simplification 1:
-1911×1
= -1911 + Show More
-1911×1
= (-19)×111×1
= -1911

Simplification 2:
14144×1
= 14144 + Show More
-1911×1
= (-19)×111×1
= -1911

Simplification 3:
60988×4
= 60922 + Show More
-1911×1
= (-19)×111×1
= -1911


= 128344 - 12X4 - 2X5+ Show More
-1911+14144+60922
= 128344 + Show More
-1911 + 14144 + 60922
= (-19)×4 + 141×1 + 609×244
= (-76)+141+121844
= 128344


R.H.S.
= 17

Subtracting same quantity from both sides of the above equation,
⇒ [128344 - 12X4 - 2X5] - [128344] = [17] - [128344]
⇒ - 12X4 - 2X5 = - 53544+ Show More
L.H.S.
= 128344 - 12X4 - 2X5 - 128344
= 0 - 12X4 - 2X5+ Show More
128344 + -128344
= 0 + Show More
128344 + -128344
= 1283 + (-1283)44
= 044
= 0

R.H.S.
= 17 - 128344
= - 53544+ Show More
17 + -128344
= -53544 + Show More
17 + -128344
= 17×44 + (-1283)×144
= 748+(-1283)44
= -53544

Dividing both sides of the above equation by same number,
⇒ [- 12X4 - 2X5] ÷ [- 1] = [- 53544] ÷ [- 1]
⇒ 12X4 + 2X5 = 53544+ Show More
L.H.S.
= [- 12X4 - 2X5]÷-1
= [-12X4÷-1] + [-2X5÷-1]
= 12X4 + 2X5 + Show More
Simplification 1:
-12X4÷(-1)
= [-12÷(-1)]X4
= 12X4 + Show More
-12 ÷ (-1)
= -12×1-1
= 12×-1-1
= 12×1
= 12

Simplification 2:
(-2)X5÷(-1)
= [(-2)÷(-1)]X5
= 2X5 + Show More
(-2) ÷ (-1)
= (-2)×1-1
= 2×-1-1
= 2×1
= 2



R.H.S.
= [- 53544]÷-1
= [-53544÷-1]
= 53544 + Show More
-53544÷(-1)
= 53544 + Show More
-53544 ÷ (-1)
= -53544×1-1
= 53544×-1-1
= 53544×1
= 53544

Eliminating variable X4 from equation 17 and 18
10X5 = 149722   ... 19+ Show More
We have,
-2X4 +2X5 = 42722
12X4 +2X5 = 53544


Multiplying the second equation by 4 we get,

-2X4 +2X5 = 42722 
2X4 +8X5 = 53511+ Show More
L.H.S.
= [12X4 + 2X5]×4
= [12X4×4] + [2X5×4]
= 2X4 + 8X5 + Show More
Simplification 1:
12X4×4
= [12×4]X4
= 2X4 + Show More
12×4
= 11×2×2×21
= 11×2×2×21
= 11×21
= 2

Simplification 2:
2X5×4
= [2×4]X5
= 8X5 + Show More
2×4
= 8



R.H.S.
= [53544]×4
= [53544×4]
= 53511 + Show More
53544×4
= 53511 + Show More
53544×4
= 53511×4×1×41
= 53511×4×1×41
= 53511×11
= 53511


Adding these two equations we get,

 -2X4 +2X5 = 42722 
(+)2X4 +8X5 = 53511 
   +10X5 = 149722+ Show More
L.H.S.
= [- 2X4 + 2X5] + [2X4 + 8X5]
= - 2X4 + 2X5 + 2X4 + 8X5
= - 2X4 + 2X4 + 2X5 + 8X5
= 0 + 10X5+ Show More
Simplification 1:
(-2)X4 + 2X4
= [(-2) + 2]X4
= 0X4 + Show More
-2 + 2
= 0

Simplification 2:
2X5 + 8X5
= [2 + 8]X5
= 10X5 + Show More
2 + 8
= 10


= 10X5

R.H.S.
= [42722] + [53511]
= 42722 + 53511
= 149722+ Show More
42722 + 53511
= 149722 + Show More
42722 + 53511
= 427×11 + 535×2222×11
= 4697+11770242
= 16467242
= 149722×1111
= 149722×1
= 149722

Solving equation 19 for variable X5 we get,
X5 = 1497220  Ans.    ... 19+ Show More
10X5 = 149722
Dividing both sides of the above equation by same number,
⇒ [10X5] ÷ [10] = [149722] ÷ [10]
⇒ X5 = 1497220+ Show More
L.H.S.
= [10X5]÷10
= [10X5÷10]
= X5 + Show More
10X5÷10
= [10÷10]X5
= 1X5 + Show More
10 ÷ 10
= 10×110
= 1×101×11×10
= 1×101×11×10
= 11×11
= 1


R.H.S.
= [149722]÷10
= [149722÷10]
= 1497220 + Show More
149722÷10
= 1497220 + Show More
149722 ÷ 10
= 149722×110
= 1497220
Substituting the value of variable X5 from equation 19 into 17 we get,
X4 = - 2910  Ans.    ... 20+ Show More
Substituting the following equation,
X5 = 1497220
into
- 2X4 + 2X5 = 42722
we have,
⇒  - 2X4 + 2×[1497220] = 42722
⇒ - 2X4 + 1497110 = 42722+ Show More
L.H.S.
=  - 2X4 + 2×[1497220]
= - 2X4 + [2×1497220]
= - 2X4 + 1497110+ Show More
1497220×2
= 1497110 + Show More
1497220×2
= 1497110×2×1×21
= 1497110×2×1×21
= 1497110×11
= 1497110


R.H.S.
= 42722

Subtracting same quantity from both sides of the above equation,
⇒ [- 2X4 + 1497110] - [1497110] = [42722] - [1497110]
⇒ - 2X4 = 295+ Show More
L.H.S.
= - 2X4 + 1497110 - 1497110
= - 2X4 + 0+ Show More
1497110 + -1497110
= 0 + Show More
1497110 + -1497110
= 1497 + (-1497)110
= 0110
= 0

R.H.S.
= 42722 - 1497110
= 295+ Show More
42722 + -1497110
= 295 + Show More
42722 + -1497110
= 427×110 + (-1497)×2222×110
= 46970+(-32934)2420
= 140362420
= 295×484484
= 295×1
= 295

Dividing both sides of the above equation by same number,
⇒ [- 2X4] ÷ [- 2] = [295] ÷ [- 2]
⇒ X4 = - 2910+ Show More
L.H.S.
= [- 2X4]÷-2
= [-2X4÷-2]
= X4 + Show More
(-2)X4÷(-2)
= [(-2)÷(-2)]X4
= 1X4 + Show More
(-2) ÷ (-2)
= (-2)×1-2
= 1×-21×11×-2
= 1×-21×11×-2
= 11×11
= 1


R.H.S.
= [295]÷-2
= [295÷-2]
= - 2910 + Show More
295÷(-2)
= -2910 + Show More
295 ÷ (-2)
= 295×1-2
= -2910×-1-1
= -2910×1
= -2910

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