2(x-4)(x-4)-7=13

Solution for 2(x-4)(x-4)-7=13 equation:

Simplifying
2(x + -4)(x + -4) + -7 = 13

Reorder the terms:
2(-4 + x)(x + -4) + -7 = 13

Reorder the terms:
2(-4 + x)(-4 + x) + -7 = 13

Multiply (-4 + x) * (-4 + x)
2(-4(-4 + x) + x(-4 + x)) + -7 = 13
2((-4 * -4 + x * -4) + x(-4 + x)) + -7 = 13
2((16 + -4x) + x(-4 + x)) + -7 = 13
2(16 + -4x + (-4 * x + x * x)) + -7 = 13
2(16 + -4x + (-4x + x2)) + -7 = 13

Combine like terms: -4x + -4x = -8x
2(16 + -8x + x2) + -7 = 13
(16 * 2 + -8x * 2 + x2 * 2) + -7 = 13
(32 + -16x + 2x2) + -7 = 13

Reorder the terms:
32 + -7 + -16x + 2x2 = 13

Combine like terms: 32 + -7 = 25
25 + -16x + 2x2 = 13

Solving
25 + -16x + 2x2 = 13

Solving for variable 'x'.

Reorder the terms:
25 + -13 + -16x + 2x2 = 13 + -13

Combine like terms: 25 + -13 = 12
12 + -16x + 2x2 = 13 + -13

Combine like terms: 13 + -13 = 0
12 + -16x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -8x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + -8x + x2)' equal to zero and attempt to solve:

Simplifying
6 + -8x + x2 = 0

Solving
6 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -8x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -8x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -8x + x2 = 0 + -6
-8x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-8x + x2 = -6

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = -6 + 16

Reorder the terms:
16 + -8x + x2 = -6 + 16

Combine like terms: -6 + 16 = 10
16 + -8x + x2 = 10

Factor a perfect square on the left side:
(x + -4)(x + -4) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + -4) equal to 3.16227766 and -3.16227766.

Subproblem 1
x + -4 = 3.16227766

Simplifying
x + -4 = 3.16227766

Reorder the terms:
-4 + x = 3.16227766

Solving
-4 + x = 3.16227766

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 3.16227766 + 4

Combine like terms: -4 + 4 = 0
0 + x = 3.16227766 + 4
x = 3.16227766 + 4

Combine like terms: 3.16227766 + 4 = 7.16227766
x = 7.16227766

Simplifying
x = 7.16227766

Subproblem 2
x + -4 = -3.16227766

Simplifying
x + -4 = -3.16227766

Reorder the terms:
-4 + x = -3.16227766

Solving
-4 + x = -3.16227766

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -3.16227766 + 4

Combine like terms: -4 + 4 = 0
0 + x = -3.16227766 + 4
x = -3.16227766 + 4

Combine like terms: -3.16227766 + 4 = 0.83772234
x = 0.83772234

Simplifying
x = 0.83772234

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.16227766, 0.83772234}
Solution
x = {7.16227766, 0.83772234}