8x^2+0.25x-86=0

Solution for 8x^2+0.25x-86=0 equation:

Simplifying
8x2 + 0.25x + -86 = 0

Reorder the terms:
-86 + 0.25x + 8x2 = 0

Solving
-86 + 0.25x + 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'.
-10.75 + 0.03125x + x2 = 0

Move the constant term to the right:

Add '10.75' to each side of the equation.
-10.75 + 0.03125x + 10.75 + x2 = 0 + 10.75

Reorder the terms:
-10.75 + 10.75 + 0.03125x + x2 = 0 + 10.75

Combine like terms: -10.75 + 10.75 = 0.00
0.00 + 0.03125x + x2 = 0 + 10.75
0.03125x + x2 = 0 + 10.75

Combine like terms: 0 + 10.75 = 10.75
0.03125x + x2 = 10.75

The x term is 0.03125x.  Take half its coefficient (0.015625).
Square it (0.000244140625) and add it to both sides.

Add '0.000244140625' to each side of the equation.
0.03125x + 0.000244140625 + x2 = 10.75 + 0.000244140625

Reorder the terms:
0.000244140625 + 0.03125x + x2 = 10.75 + 0.000244140625

Combine like terms: 10.75 + 0.000244140625 = 10.750244140625
0.000244140625 + 0.03125x + x2 = 10.750244140625

Factor a perfect square on the left side:
(x + 0.015625)(x + 0.015625) = 10.750244140625

Calculate the square root of the right side: 3.278756493

Break this problem into two subproblems by setting 
(x + 0.015625) equal to 3.278756493 and -3.278756493.

Subproblem 1
x + 0.015625 = 3.278756493

Simplifying
x + 0.015625 = 3.278756493

Reorder the terms:
0.015625 + x = 3.278756493

Solving
0.015625 + x = 3.278756493

Solving for variable 'x'.

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

Add '-0.015625' to each side of the equation.
0.015625 + -0.015625 + x = 3.278756493 + -0.015625

Combine like terms: 0.015625 + -0.015625 = 0.000000
0.000000 + x = 3.278756493 + -0.015625
x = 3.278756493 + -0.015625

Combine like terms: 3.278756493 + -0.015625 = 3.263131493
x = 3.263131493

Simplifying
x = 3.263131493

Subproblem 2
x + 0.015625 = -3.278756493

Simplifying
x + 0.015625 = -3.278756493

Reorder the terms:
0.015625 + x = -3.278756493

Solving
0.015625 + x = -3.278756493

Solving for variable 'x'.

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

Add '-0.015625' to each side of the equation.
0.015625 + -0.015625 + x = -3.278756493 + -0.015625

Combine like terms: 0.015625 + -0.015625 = 0.000000
0.000000 + x = -3.278756493 + -0.015625
x = -3.278756493 + -0.015625

Combine like terms: -3.278756493 + -0.015625 = -3.294381493
x = -3.294381493

Simplifying
x = -3.294381493

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.263131493, -3.294381493}