-0.25x^2-x=-8

Solution for -0.25x^2-x=-8 equation:

Simplifying
-0.25x2 + -1x = -8

Reorder the terms:
-1x + -0.25x2 = -8

Solving
-1x + -0.25x2 = -8

Solving for variable 'x'.

Reorder the terms:
8 + -1x + -0.25x2 = -8 + 8

Combine like terms: -8 + 8 = 0
8 + -1x + -0.25x2 = 0

Begin completing the square.  Divide all terms by
-0.25 the coefficient of the squared term: 

Divide each side by '-0.25'.
-32 + 4x + x2 = 0

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + 4x + 32 + x2 = 0 + 32

Reorder the terms:
-32 + 32 + 4x + x2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 4x + x2 = 0 + 32
4x + x2 = 0 + 32

Combine like terms: 0 + 32 = 32
4x + x2 = 32

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 32 + 4

Reorder the terms:
4 + 4x + x2 = 32 + 4

Combine like terms: 32 + 4 = 36
4 + 4x + x2 = 36

Factor a perfect square on the left side:
(x + 2)(x + 2) = 36

Calculate the square root of the right side: 6

Break this problem into two subproblems by setting 
(x + 2) equal to 6 and -6.

Subproblem 1
x + 2 = 6

Simplifying
x + 2 = 6

Reorder the terms:
2 + x = 6

Solving
2 + x = 6

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 6 + -2

Combine like terms: 2 + -2 = 0
0 + x = 6 + -2
x = 6 + -2

Combine like terms: 6 + -2 = 4
x = 4

Simplifying
x = 4

Subproblem 2
x + 2 = -6

Simplifying
x + 2 = -6

Reorder the terms:
2 + x = -6

Solving
2 + x = -6

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -6 + -2

Combine like terms: 2 + -2 = 0
0 + x = -6 + -2
x = -6 + -2

Combine like terms: -6 + -2 = -8
x = -8

Simplifying
x = -8

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4, -8}