(x*x)-2x+1=10x-31

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Solution for (x*x)-2x+1=10x-31 equation: 


Simplifying
(x * x) + -2x + 1 = 10x + -31

Multiply x * x
(x2) + -2x + 1 = 10x + -31
x2 + -2x + 1 = 10x + -31

Reorder the terms:
1 + -2x + x2 = 10x + -31

Reorder the terms:
1 + -2x + x2 = -31 + 10x

Solving
1 + -2x + x2 = -31 + 10x

Solving for variable 'x'.

Reorder the terms:
1 + 31 + -2x + -10x + x2 = -31 + 10x + 31 + -10x

Combine like terms: 1 + 31 = 32
32 + -2x + -10x + x2 = -31 + 10x + 31 + -10x

Combine like terms: -2x + -10x = -12x
32 + -12x + x2 = -31 + 10x + 31 + -10x

Reorder the terms:
32 + -12x + x2 = -31 + 31 + 10x + -10x

Combine like terms: -31 + 31 = 0
32 + -12x + x2 = 0 + 10x + -10x
32 + -12x + x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
32 + -12x + x2 = 0

Factor a trinomial.
(4 + -1x)(8 + -1x) = 0


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {4, 8}

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