-8x^2+11x+13=0

Solution for -8x^2+11x+13=0 equation:

Simplifying
-8x2 + 11x + 13 = 0

Reorder the terms:
13 + 11x + -8x2 = 0

Solving
13 + 11x + -8x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-1.625 + -1.375x + x2 = 0

Move the constant term to the right:

Add '1.625' to each side of the equation.
-1.625 + -1.375x + 1.625 + x2 = 0 + 1.625

Reorder the terms:
-1.625 + 1.625 + -1.375x + x2 = 0 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + -1.375x + x2 = 0 + 1.625
-1.375x + x2 = 0 + 1.625

Combine like terms: 0 + 1.625 = 1.625
-1.375x + x2 = 1.625

The x term is -1.375x.  Take half its coefficient (-0.6875).
Square it (0.47265625) and add it to both sides.

Add '0.47265625' to each side of the equation.
-1.375x + 0.47265625 + x2 = 1.625 + 0.47265625

Reorder the terms:
0.47265625 + -1.375x + x2 = 1.625 + 0.47265625

Combine like terms: 1.625 + 0.47265625 = 2.09765625
0.47265625 + -1.375x + x2 = 2.09765625

Factor a perfect square on the left side:
(x + -0.6875)(x + -0.6875) = 2.09765625

Calculate the square root of the right side: 1.448328778

Break this problem into two subproblems by setting 
(x + -0.6875) equal to 1.448328778 and -1.448328778.

Subproblem 1
x + -0.6875 = 1.448328778

Simplifying
x + -0.6875 = 1.448328778

Reorder the terms:
-0.6875 + x = 1.448328778

Solving
-0.6875 + x = 1.448328778

Solving for variable 'x'.

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

Add '0.6875' to each side of the equation.
-0.6875 + 0.6875 + x = 1.448328778 + 0.6875

Combine like terms: -0.6875 + 0.6875 = 0.0000
0.0000 + x = 1.448328778 + 0.6875
x = 1.448328778 + 0.6875

Combine like terms: 1.448328778 + 0.6875 = 2.135828778
x = 2.135828778

Simplifying
x = 2.135828778

Subproblem 2
x + -0.6875 = -1.448328778

Simplifying
x + -0.6875 = -1.448328778

Reorder the terms:
-0.6875 + x = -1.448328778

Solving
-0.6875 + x = -1.448328778

Solving for variable 'x'.

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

Add '0.6875' to each side of the equation.
-0.6875 + 0.6875 + x = -1.448328778 + 0.6875

Combine like terms: -0.6875 + 0.6875 = 0.0000
0.0000 + x = -1.448328778 + 0.6875
x = -1.448328778 + 0.6875

Combine like terms: -1.448328778 + 0.6875 = -0.760828778
x = -0.760828778

Simplifying
x = -0.760828778

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.135828778, -0.760828778}