-(x+8)(x-9)=-52

Solution for -(x+8)(x-9)=-52 equation:

Simplifying
-1(x + 8)(x + -9) = -52

Reorder the terms:
-1(8 + x)(x + -9) = -52

Reorder the terms:
-1(8 + x)(-9 + x) = -52

Multiply (8 + x) * (-9 + x)
-1(8(-9 + x) + x(-9 + x)) = -52
-1((-9 * 8 + x * 8) + x(-9 + x)) = -52
-1((-72 + 8x) + x(-9 + x)) = -52
-1(-72 + 8x + (-9 * x + x * x)) = -52
-1(-72 + 8x + (-9x + x2)) = -52

Combine like terms: 8x + -9x = -1x
-1(-72 + -1x + x2) = -52
(-72 * -1 + -1x * -1 + x2 * -1) = -52
(72 + 1x + -1x2) = -52

Solving
72 + 1x + -1x2 = -52

Solving for variable 'x'.

Reorder the terms:
72 + 52 + 1x + -1x2 = -52 + 52

Combine like terms: 72 + 52 = 124
124 + 1x + -1x2 = -52 + 52

Combine like terms: -52 + 52 = 0
124 + 1x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-124 + -1x + x2 = 0

Move the constant term to the right:

Add '124' to each side of the equation.
-124 + -1x + 124 + x2 = 0 + 124

Reorder the terms:
-124 + 124 + -1x + x2 = 0 + 124

Combine like terms: -124 + 124 = 0
0 + -1x + x2 = 0 + 124
-1x + x2 = 0 + 124

Combine like terms: 0 + 124 = 124
-1x + x2 = 124

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 124 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 124 + 0.25

Combine like terms: 124 + 0.25 = 124.25
0.25 + -1x + x2 = 124.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 124.25

Calculate the square root of the right side: 11.146748405

Break this problem into two subproblems by setting 
(x + -0.5) equal to 11.146748405 and -11.146748405.

Subproblem 1
x + -0.5 = 11.146748405

Simplifying
x + -0.5 = 11.146748405

Reorder the terms:
-0.5 + x = 11.146748405

Solving
-0.5 + x = 11.146748405

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 11.146748405 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 11.146748405 + 0.5
x = 11.146748405 + 0.5

Combine like terms: 11.146748405 + 0.5 = 11.646748405
x = 11.646748405

Simplifying
x = 11.646748405

Subproblem 2
x + -0.5 = -11.146748405

Simplifying
x + -0.5 = -11.146748405

Reorder the terms:
-0.5 + x = -11.146748405

Solving
-0.5 + x = -11.146748405

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -11.146748405 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -11.146748405 + 0.5
x = -11.146748405 + 0.5

Combine like terms: -11.146748405 + 0.5 = -10.646748405
x = -10.646748405

Simplifying
x = -10.646748405

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.646748405, -10.646748405}