(x-8)(x+9)=10

Solution for (x-8)(x+9)=10 equation:

Simplifying
(x + -8)(x + 9) = 10

Reorder the terms:
(-8 + x)(x + 9) = 10

Reorder the terms:
(-8 + x)(9 + x) = 10

Multiply (-8 + x) * (9 + x)
(-8(9 + x) + x(9 + x)) = 10
((9 * -8 + x * -8) + x(9 + x)) = 10
((-72 + -8x) + x(9 + x)) = 10
(-72 + -8x + (9 * x + x * x)) = 10
(-72 + -8x + (9x + x2)) = 10

Combine like terms: -8x + 9x = 1x
(-72 + 1x + x2) = 10

Solving
-72 + 1x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
-72 + -10 + 1x + x2 = 10 + -10

Combine like terms: -72 + -10 = -82
-82 + 1x + x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-82 + 1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '82' to each side of the equation.
-82 + 1x + 82 + x2 = 0 + 82

Reorder the terms:
-82 + 82 + 1x + x2 = 0 + 82

Combine like terms: -82 + 82 = 0
0 + 1x + x2 = 0 + 82
1x + x2 = 0 + 82

Combine like terms: 0 + 82 = 82
1x + x2 = 82

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.
x + 0.25 + x2 = 82 + 0.25

Reorder the terms:
0.25 + x + x2 = 82 + 0.25

Combine like terms: 82 + 0.25 = 82.25
0.25 + x + x2 = 82.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 82.25

Calculate the square root of the right side: 9.069178574

Break this problem into two subproblems by setting 
(x + 0.5) equal to 9.069178574 and -9.069178574.

Subproblem 1
x + 0.5 = 9.069178574

Simplifying
x + 0.5 = 9.069178574

Reorder the terms:
0.5 + x = 9.069178574

Solving
0.5 + x = 9.069178574

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 = 9.069178574 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 9.069178574 + -0.5
x = 9.069178574 + -0.5

Combine like terms: 9.069178574 + -0.5 = 8.569178574
x = 8.569178574

Simplifying
x = 8.569178574

Subproblem 2
x + 0.5 = -9.069178574

Simplifying
x + 0.5 = -9.069178574

Reorder the terms:
0.5 + x = -9.069178574

Solving
0.5 + x = -9.069178574

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 = -9.069178574 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -9.069178574 + -0.5
x = -9.069178574 + -0.5

Combine like terms: -9.069178574 + -0.5 = -9.569178574
x = -9.569178574

Simplifying
x = -9.569178574

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.569178574, -9.569178574}