(x-4)(x+4)=(x+5)2

Solution for (x-4)(x+4)=(x+5)2 equation:

Simplifying
(x + -4)(x + 4) = (x + 5) * 2

Reorder the terms:
(-4 + x)(x + 4) = (x + 5) * 2

Reorder the terms:
(-4 + x)(4 + x) = (x + 5) * 2

Multiply (-4 + x) * (4 + x)
(-4(4 + x) + x(4 + x)) = (x + 5) * 2
((4 * -4 + x * -4) + x(4 + x)) = (x + 5) * 2
((-16 + -4x) + x(4 + x)) = (x + 5) * 2
(-16 + -4x + (4 * x + x * x)) = (x + 5) * 2
(-16 + -4x + (4x + x2)) = (x + 5) * 2

Combine like terms: -4x + 4x = 0
(-16 + 0 + x2) = (x + 5) * 2
(-16 + x2) = (x + 5) * 2

Reorder the terms:
-16 + x2 = (5 + x) * 2

Reorder the terms for easier multiplication:
-16 + x2 = 2(5 + x)
-16 + x2 = (5 * 2 + x * 2)
-16 + x2 = (10 + 2x)

Solving
-16 + x2 = 10 + 2x

Solving for variable 'x'.

Reorder the terms:
-16 + -10 + -2x + x2 = 10 + 2x + -10 + -2x

Combine like terms: -16 + -10 = -26
-26 + -2x + x2 = 10 + 2x + -10 + -2x

Reorder the terms:
-26 + -2x + x2 = 10 + -10 + 2x + -2x

Combine like terms: 10 + -10 = 0
-26 + -2x + x2 = 0 + 2x + -2x
-26 + -2x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-26 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '26' to each side of the equation.
-26 + -2x + 26 + x2 = 0 + 26

Reorder the terms:
-26 + 26 + -2x + x2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + -2x + x2 = 0 + 26
-2x + x2 = 0 + 26

Combine like terms: 0 + 26 = 26
-2x + x2 = 26

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 26 + 1

Reorder the terms:
1 + -2x + x2 = 26 + 1

Combine like terms: 26 + 1 = 27
1 + -2x + x2 = 27

Factor a perfect square on the left side:
(x + -1)(x + -1) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(x + -1) equal to 5.196152423 and -5.196152423.

Subproblem 1
x + -1 = 5.196152423

Simplifying
x + -1 = 5.196152423

Reorder the terms:
-1 + x = 5.196152423

Solving
-1 + x = 5.196152423

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 5.196152423 + 1

Combine like terms: -1 + 1 = 0
0 + x = 5.196152423 + 1
x = 5.196152423 + 1

Combine like terms: 5.196152423 + 1 = 6.196152423
x = 6.196152423

Simplifying
x = 6.196152423

Subproblem 2
x + -1 = -5.196152423

Simplifying
x + -1 = -5.196152423

Reorder the terms:
-1 + x = -5.196152423

Solving
-1 + x = -5.196152423

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -5.196152423 + 1

Combine like terms: -1 + 1 = 0
0 + x = -5.196152423 + 1
x = -5.196152423 + 1

Combine like terms: -5.196152423 + 1 = -4.196152423
x = -4.196152423

Simplifying
x = -4.196152423

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.196152423, -4.196152423}