8x^2+2x-11=0

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


Simplifying
8x2 + 2x + -11 = 0

Reorder the terms:
-11 + 2x + 8x2 = 0

Solving
-11 + 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'.
-1.375 + 0.25x + x2 = 0

Move the constant term to the right:

Add '1.375' to each side of the equation.
-1.375 + 0.25x + 1.375 + x2 = 0 + 1.375

Reorder the terms:
-1.375 + 1.375 + 0.25x + x2 = 0 + 1.375

Combine like terms: -1.375 + 1.375 = 0.000
0.000 + 0.25x + x2 = 0 + 1.375
0.25x + x2 = 0 + 1.375

Combine like terms: 0 + 1.375 = 1.375
0.25x + x2 = 1.375

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 = 1.375 + 0.015625

Reorder the terms:
0.015625 + 0.25x + x2 = 1.375 + 0.015625

Combine like terms: 1.375 + 0.015625 = 1.390625
0.015625 + 0.25x + x2 = 1.390625

Factor a perfect square on the left side:
(x + 0.125)(x + 0.125) = 1.390625

Calculate the square root of the right side: 1.179247642

Break this problem into two subproblems by setting 
(x + 0.125) equal to 1.179247642 and -1.179247642.


Subproblem 1
x + 0.125 = 1.179247642

Simplifying
x + 0.125 = 1.179247642

Reorder the terms:
0.125 + x = 1.179247642

Solving
0.125 + x = 1.179247642

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 = 1.179247642 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + x = 1.179247642 + -0.125
x = 1.179247642 + -0.125

Combine like terms: 1.179247642 + -0.125 = 1.054247642
x = 1.054247642

Simplifying
x = 1.054247642


Subproblem 2
x + 0.125 = -1.179247642

Simplifying
x + 0.125 = -1.179247642

Reorder the terms:
0.125 + x = -1.179247642

Solving
0.125 + x = -1.179247642

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 = -1.179247642 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + x = -1.179247642 + -0.125
x = -1.179247642 + -0.125

Combine like terms: -1.179247642 + -0.125 = -1.304247642
x = -1.304247642

Simplifying
x = -1.304247642


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.054247642, -1.304247642}

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