(10)(10)-(x+2)(x-1)=86

Solution for (10)(10)-(x+2)(x-1)=86 equation:

Simplifying
(10)(10) + -1(x + 2)(x + -1) = 86

Multiply 10 * 10
100 + -1(x + 2)(x + -1) = 86

Reorder the terms:
100 + -1(2 + x)(x + -1) = 86

Reorder the terms:
100 + -1(2 + x)(-1 + x) = 86

Multiply (2 + x) * (-1 + x)
100 + -1(2(-1 + x) + x(-1 + x)) = 86
100 + -1((-1 * 2 + x * 2) + x(-1 + x)) = 86
100 + -1((-2 + 2x) + x(-1 + x)) = 86
100 + -1(-2 + 2x + (-1 * x + x * x)) = 86
100 + -1(-2 + 2x + (-1x + x2)) = 86

Combine like terms: 2x + -1x = 1x
100 + -1(-2 + 1x + x2) = 86
100 + (-2 * -1 + 1x * -1 + x2 * -1) = 86
100 + (2 + -1x + -1x2) = 86

Combine like terms: 100 + 2 = 102
102 + -1x + -1x2 = 86

Solving
102 + -1x + -1x2 = 86

Solving for variable 'x'.

Reorder the terms:
102 + -86 + -1x + -1x2 = 86 + -86

Combine like terms: 102 + -86 = 16
16 + -1x + -1x2 = 86 + -86

Combine like terms: 86 + -86 = 0
16 + -1x + -1x2 = 0

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

Divide each side by '-1'.
-16 + x + x2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + x + x2 = 0 + 16
x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
x + x2 = 16

The x term is x.  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.
 + 0.25 + x2 = 16 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 16 + 0.25

Combine like terms: 16 + 0.25 = 16.25
1.25 + x2 = 16.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 16.25

Calculate the square root of the right side: 4.031128874

Break this problem into two subproblems by setting 
(x + 0.5) equal to 4.031128874 and -4.031128874.

Subproblem 1
x + 0.5 = 4.031128874

Simplifying
x + 0.5 = 4.031128874

Reorder the terms:
0.5 + x = 4.031128874

Solving
0.5 + x = 4.031128874

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 = 4.031128874 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 4.031128874 + -0.5
x = 4.031128874 + -0.5

Combine like terms: 4.031128874 + -0.5 = 3.531128874
x = 3.531128874

Simplifying
x = 3.531128874

Subproblem 2
x + 0.5 = -4.031128874

Simplifying
x + 0.5 = -4.031128874

Reorder the terms:
0.5 + x = -4.031128874

Solving
0.5 + x = -4.031128874

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 = -4.031128874 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -4.031128874 + -0.5
x = -4.031128874 + -0.5

Combine like terms: -4.031128874 + -0.5 = -4.531128874
x = -4.531128874

Simplifying
x = -4.531128874

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.531128874, -4.531128874}