-8x^2-2x+87=0

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Solution for -8x^2-2x+87=0 equation: 


Simplifying
-8x2 + -2x + 87 = 0

Reorder the terms:
87 + -2x + -8x2 = 0

Solving
87 + -2x + -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'.
-10.875 + 0.25x + x2 = 0

Move the constant term to the right:

Add '10.875' to each side of the equation.
-10.875 + 0.25x + 10.875 + x2 = 0 + 10.875

Reorder the terms:
-10.875 + 10.875 + 0.25x + x2 = 0 + 10.875

Combine like terms: -10.875 + 10.875 = 0.000
0.000 + 0.25x + x2 = 0 + 10.875
0.25x + x2 = 0 + 10.875

Combine like terms: 0 + 10.875 = 10.875
0.25x + x2 = 10.875

The x term is 0.25x.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25x + 0.015625 + x2 = 10.875 + 0.015625

Reorder the terms:
0.015625 + 0.25x + x2 = 10.875 + 0.015625

Combine like terms: 10.875 + 0.015625 = 10.890625
0.015625 + 0.25x + x2 = 10.890625

Factor a perfect square on the left side:
(x + 0.125)(x + 0.125) = 10.890625

Calculate the square root of the right side: 3.300094696

Break this problem into two subproblems by setting 
(x + 0.125) equal to 3.300094696 and -3.300094696.


Subproblem 1
x + 0.125 = 3.300094696

Simplifying
x + 0.125 = 3.300094696

Reorder the terms:
0.125 + x = 3.300094696

Solving
0.125 + x = 3.300094696

Solving for variable 'x'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + x = 3.300094696 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + x = 3.300094696 + -0.125
x = 3.300094696 + -0.125

Combine like terms: 3.300094696 + -0.125 = 3.175094696
x = 3.175094696

Simplifying
x = 3.175094696


Subproblem 2
x + 0.125 = -3.300094696

Simplifying
x + 0.125 = -3.300094696

Reorder the terms:
0.125 + x = -3.300094696

Solving
0.125 + x = -3.300094696

Solving for variable 'x'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + x = -3.300094696 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + x = -3.300094696 + -0.125
x = -3.300094696 + -0.125

Combine like terms: -3.300094696 + -0.125 = -3.425094696
x = -3.425094696

Simplifying
x = -3.425094696


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.175094696, -3.425094696}

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