2(x^2-10x+25)+13=31

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Solution for 2(x^2-10x+25)+13=31 equation: 


Simplifying
2(x2 + -10x + 25) + 13 = 31

Reorder the terms:
2(25 + -10x + x2) + 13 = 31
(25 * 2 + -10x * 2 + x2 * 2) + 13 = 31
(50 + -20x + 2x2) + 13 = 31

Reorder the terms:
50 + 13 + -20x + 2x2 = 31

Combine like terms: 50 + 13 = 63
63 + -20x + 2x2 = 31

Solving
63 + -20x + 2x2 = 31

Solving for variable 'x'.

Reorder the terms:
63 + -31 + -20x + 2x2 = 31 + -31

Combine like terms: 63 + -31 = 32
32 + -20x + 2x2 = 31 + -31

Combine like terms: 31 + -31 = 0
32 + -20x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + -10x + x2) = 0

Factor a trinomial.
2((2 + -1x)(8 + -1x)) = 0

Ignore the factor 2.

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

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 = {2, 8}

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