8x^2-2x-79=0

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Solution for 8x^2-2x-79=0 equation: 


Simplifying
8x2 + -2x + -79 = 0

Reorder the terms:
-79 + -2x + 8x2 = 0

Solving
-79 + -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'.
-9.875 + -0.25x + x2 = 0

Move the constant term to the right:

Add '9.875' to each side of the equation.
-9.875 + -0.25x + 9.875 + x2 = 0 + 9.875

Reorder the terms:
-9.875 + 9.875 + -0.25x + x2 = 0 + 9.875

Combine like terms: -9.875 + 9.875 = 0.000
0.000 + -0.25x + x2 = 0 + 9.875
-0.25x + x2 = 0 + 9.875

Combine like terms: 0 + 9.875 = 9.875
-0.25x + x2 = 9.875

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 = 9.875 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 9.875 + 0.015625

Combine like terms: 9.875 + 0.015625 = 9.890625
0.015625 + -0.25x + x2 = 9.890625

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 9.890625

Calculate the square root of the right side: 3.144936406

Break this problem into two subproblems by setting 
(x + -0.125) equal to 3.144936406 and -3.144936406.


Subproblem 1
x + -0.125 = 3.144936406

Simplifying
x + -0.125 = 3.144936406

Reorder the terms:
-0.125 + x = 3.144936406

Solving
-0.125 + x = 3.144936406

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 = 3.144936406 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = 3.144936406 + 0.125
x = 3.144936406 + 0.125

Combine like terms: 3.144936406 + 0.125 = 3.269936406
x = 3.269936406

Simplifying
x = 3.269936406


Subproblem 2
x + -0.125 = -3.144936406

Simplifying
x + -0.125 = -3.144936406

Reorder the terms:
-0.125 + x = -3.144936406

Solving
-0.125 + x = -3.144936406

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 = -3.144936406 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + x = -3.144936406 + 0.125
x = -3.144936406 + 0.125

Combine like terms: -3.144936406 + 0.125 = -3.019936406
x = -3.019936406

Simplifying
x = -3.019936406


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.269936406, -3.019936406}

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