5x^2-10x-8=0

Solution for 5x^2-10x-8=0 equation:

Simplifying
5x2 + -10x + -8 = 0

Reorder the terms:
-8 + -10x + 5x2 = 0

Solving
-8 + -10x + 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 + -2x + x2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + -2x + 1.6 + x2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + -2x + x2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + -2x + x2 = 0 + 1.6
-2x + x2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
-2x + x2 = 1.6

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 1.6 + 1

Reorder the terms:
1 + -2x + x2 = 1.6 + 1

Combine like terms: 1.6 + 1 = 2.6
1 + -2x + x2 = 2.6

Factor a perfect square on the left side:
(x + -1)(x + -1) = 2.6

Calculate the square root of the right side: 1.61245155

Break this problem into two subproblems by setting 
(x + -1) equal to 1.61245155 and -1.61245155.

Subproblem 1
x + -1 = 1.61245155

Simplifying
x + -1 = 1.61245155

Reorder the terms:
-1 + x = 1.61245155

Solving
-1 + x = 1.61245155

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 1.61245155 + 1

Combine like terms: -1 + 1 = 0
0 + x = 1.61245155 + 1
x = 1.61245155 + 1

Combine like terms: 1.61245155 + 1 = 2.61245155
x = 2.61245155

Simplifying
x = 2.61245155

Subproblem 2
x + -1 = -1.61245155

Simplifying
x + -1 = -1.61245155

Reorder the terms:
-1 + x = -1.61245155

Solving
-1 + x = -1.61245155

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -1.61245155 + 1

Combine like terms: -1 + 1 = 0
0 + x = -1.61245155 + 1
x = -1.61245155 + 1

Combine like terms: -1.61245155 + 1 = -0.61245155
x = -0.61245155

Simplifying
x = -0.61245155

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.61245155, -0.61245155}