8x^2-2x-7=0

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Solution for 8x^2-2x-7=0 equation: 


Simplifying
8x2 + -2x + -7 = 0

Reorder the terms:
-7 + -2x + 8x2 = 0

Solving
-7 + -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'.
-0.875 + -0.25x + x2 = 0

Move the constant term to the right:

Add '0.875' to each side of the equation.
-0.875 + -0.25x + 0.875 + x2 = 0 + 0.875

Reorder the terms:
-0.875 + 0.875 + -0.25x + x2 = 0 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + -0.25x + x2 = 0 + 0.875
-0.25x + x2 = 0 + 0.875

Combine like terms: 0 + 0.875 = 0.875
-0.25x + x2 = 0.875

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 = 0.875 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 0.875 + 0.015625

Combine like terms: 0.875 + 0.015625 = 0.890625
0.015625 + -0.25x + x2 = 0.890625

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 0.890625

Calculate the square root of the right side: 0.943729304

Break this problem into two subproblems by setting 
(x + -0.125) equal to 0.943729304 and -0.943729304.


Subproblem 1
x + -0.125 = 0.943729304

Simplifying
x + -0.125 = 0.943729304

Reorder the terms:
-0.125 + x = 0.943729304

Solving
-0.125 + x = 0.943729304

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 = 0.943729304 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = 0.943729304 + 0.125
x = 0.943729304 + 0.125

Combine like terms: 0.943729304 + 0.125 = 1.068729304
x = 1.068729304

Simplifying
x = 1.068729304


Subproblem 2
x + -0.125 = -0.943729304

Simplifying
x + -0.125 = -0.943729304

Reorder the terms:
-0.125 + x = -0.943729304

Solving
-0.125 + x = -0.943729304

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 = -0.943729304 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = -0.943729304 + 0.125
x = -0.943729304 + 0.125

Combine like terms: -0.943729304 + 0.125 = -0.818729304
x = -0.818729304

Simplifying
x = -0.818729304


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.068729304, -0.818729304}

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