86-(x+2)(x-1)=100

Solution for 86-(x+2)(x-1)=100 equation:

Simplifying
86 + -1(x + 2)(x + -1) = 100

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

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

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

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

Combine like terms: 86 + 2 = 88
88 + -1x + -1x2 = 100

Solving
88 + -1x + -1x2 = 100

Solving for variable 'x'.

Reorder the terms:
88 + -100 + -1x + -1x2 = 100 + -100

Combine like terms: 88 + -100 = -12
-12 + -1x + -1x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-12 + -1x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(12 + x + x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(12 + x + x2)' equal to zero and attempt to solve:

Simplifying
12 + x + x2 = 0

Solving
12 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + x + -12 + x2 = 0 + -12

Reorder the terms:
12 + -12 + x + x2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + x + x2 = 0 + -12
x + x2 = 0 + -12

Combine like terms: 0 + -12 = -12
x + x2 = -12

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.
x + 0.25 + x2 = -12 + 0.25

Reorder the terms:
0.25 + x + x2 = -12 + 0.25

Combine like terms: -12 + 0.25 = -11.75
0.25 + x + x2 = -11.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -11.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.