5x^2-5x-8=0

Solution for 5x^2-5x-8=0 equation:

Simplifying
5x2 + -5x + -8 = 0

Reorder the terms:
-8 + -5x + 5x2 = 0

Solving
-8 + -5x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-1.6 + -1x + x2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + -1x + 1.6 + x2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + -1x + x2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + -1x + x2 = 0 + 1.6
-1x + x2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
-1x + x2 = 1.6

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.
-1x + 0.25 + x2 = 1.6 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 1.6 + 0.25

Combine like terms: 1.6 + 0.25 = 1.85
0.25 + -1x + x2 = 1.85

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 1.85

Calculate the square root of the right side: 1.360147051

Break this problem into two subproblems by setting 
(x + -0.5) equal to 1.360147051 and -1.360147051.

Subproblem 1
x + -0.5 = 1.360147051

Simplifying
x + -0.5 = 1.360147051

Reorder the terms:
-0.5 + x = 1.360147051

Solving
-0.5 + x = 1.360147051

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 = 1.360147051 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 1.360147051 + 0.5
x = 1.360147051 + 0.5

Combine like terms: 1.360147051 + 0.5 = 1.860147051
x = 1.860147051

Simplifying
x = 1.860147051

Subproblem 2
x + -0.5 = -1.360147051

Simplifying
x + -0.5 = -1.360147051

Reorder the terms:
-0.5 + x = -1.360147051

Solving
-0.5 + x = -1.360147051

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 = -1.360147051 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -1.360147051 + 0.5
x = -1.360147051 + 0.5

Combine like terms: -1.360147051 + 0.5 = -0.860147051
x = -0.860147051

Simplifying
x = -0.860147051

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.860147051, -0.860147051}