0.25x^2-3x=-8

Solution for 0.25x^2-3x=-8 equation:

Simplifying
0.25x2 + -3x = -8

Reorder the terms:
-3x + 0.25x2 = -8

Solving
-3x + 0.25x2 = -8

Solving for variable 'x'.

Reorder the terms:
8 + -3x + 0.25x2 = -8 + 8

Combine like terms: -8 + 8 = 0
8 + -3x + 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 + -12x + x2 = 0

Move the constant term to the right:

Add '-32' to each side of the equation.
32 + -12x + -32 + x2 = 0 + -32

Reorder the terms:
32 + -32 + -12x + x2 = 0 + -32

Combine like terms: 32 + -32 = 0
0 + -12x + x2 = 0 + -32
-12x + x2 = 0 + -32

Combine like terms: 0 + -32 = -32
-12x + x2 = -32

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = -32 + 36

Reorder the terms:
36 + -12x + x2 = -32 + 36

Combine like terms: -32 + 36 = 4
36 + -12x + x2 = 4

Factor a perfect square on the left side:
(x + -6)(x + -6) = 4

Calculate the square root of the right side: 2

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

Subproblem 1
x + -6 = 2

Simplifying
x + -6 = 2

Reorder the terms:
-6 + x = 2

Solving
-6 + x = 2

Solving for variable 'x'.

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

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

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

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

Simplifying
x = 8

Subproblem 2
x + -6 = -2

Simplifying
x + -6 = -2

Reorder the terms:
-6 + x = -2

Solving
-6 + x = -2

Solving for variable 'x'.

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

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

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

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

Simplifying
x = 4

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