2x+31=(x+8)(x+8)

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Solution for 2x+31=(x+8)(x+8) equation: 


Simplifying
2x + 31 = (x + 8)(x + 8)

Reorder the terms:
31 + 2x = (x + 8)(x + 8)

Reorder the terms:
31 + 2x = (8 + x)(x + 8)

Reorder the terms:
31 + 2x = (8 + x)(8 + x)

Multiply (8 + x) * (8 + x)
31 + 2x = (8(8 + x) + x(8 + x))
31 + 2x = ((8 * 8 + x * 8) + x(8 + x))
31 + 2x = ((64 + 8x) + x(8 + x))
31 + 2x = (64 + 8x + (8 * x + x * x))
31 + 2x = (64 + 8x + (8x + x2))

Combine like terms: 8x + 8x = 16x
31 + 2x = (64 + 16x + x2)

Solving
31 + 2x = 64 + 16x + x2

Solving for variable 'x'.

Reorder the terms:
31 + -64 + 2x + -16x + -1x2 = 64 + 16x + x2 + -64 + -16x + -1x2

Combine like terms: 31 + -64 = -33
-33 + 2x + -16x + -1x2 = 64 + 16x + x2 + -64 + -16x + -1x2

Combine like terms: 2x + -16x = -14x
-33 + -14x + -1x2 = 64 + 16x + x2 + -64 + -16x + -1x2

Reorder the terms:
-33 + -14x + -1x2 = 64 + -64 + 16x + -16x + x2 + -1x2

Combine like terms: 64 + -64 = 0
-33 + -14x + -1x2 = 0 + 16x + -16x + x2 + -1x2
-33 + -14x + -1x2 = 16x + -16x + x2 + -1x2

Combine like terms: 16x + -16x = 0
-33 + -14x + -1x2 = 0 + x2 + -1x2
-33 + -14x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-33 + -14x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(33 + 14x + x2) = 0

Factor a trinomial.
-1((11 + x)(3 + x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(11 + x)' equal to zero and attempt to solve:

Simplifying
11 + x = 0

Solving
11 + x = 0

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

Add '-11' to each side of the equation.
11 + -11 + x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + x = 0 + -11
x = 0 + -11

Combine like terms: 0 + -11 = -11
x = -11

Simplifying
x = -11

Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {-11, -3}

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