8x^2+58x-664=0

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Solution for 8x^2+58x-664=0 equation: 


Simplifying
8x2 + 58x + -664 = 0

Reorder the terms:
-664 + 58x + 8x2 = 0

Solving
-664 + 58x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-332 + 29x + 4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-332 + 29x + 4x2)' equal to zero and attempt to solve:

Simplifying
-332 + 29x + 4x2 = 0

Solving
-332 + 29x + 4x2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-83 + 7.25x + x2 = 0

Move the constant term to the right:

Add '83' to each side of the equation.
-83 + 7.25x + 83 + x2 = 0 + 83

Reorder the terms:
-83 + 83 + 7.25x + x2 = 0 + 83

Combine like terms: -83 + 83 = 0
0 + 7.25x + x2 = 0 + 83
7.25x + x2 = 0 + 83

Combine like terms: 0 + 83 = 83
7.25x + x2 = 83

The x term is 7.25x.  Take half its coefficient (3.625).
Square it (13.140625) and add it to both sides.

Add '13.140625' to each side of the equation.
7.25x + 13.140625 + x2 = 83 + 13.140625

Reorder the terms:
13.140625 + 7.25x + x2 = 83 + 13.140625

Combine like terms: 83 + 13.140625 = 96.140625
13.140625 + 7.25x + x2 = 96.140625

Factor a perfect square on the left side:
(x + 3.625)(x + 3.625) = 96.140625

Calculate the square root of the right side: 9.805132585

Break this problem into two subproblems by setting 
(x + 3.625) equal to 9.805132585 and -9.805132585.


Subproblem 1
x + 3.625 = 9.805132585

Simplifying
x + 3.625 = 9.805132585

Reorder the terms:
3.625 + x = 9.805132585

Solving
3.625 + x = 9.805132585

Solving for variable 'x'.

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

Add '-3.625' to each side of the equation.
3.625 + -3.625 + x = 9.805132585 + -3.625

Combine like terms: 3.625 + -3.625 = 0.000
0.000 + x = 9.805132585 + -3.625
x = 9.805132585 + -3.625

Combine like terms: 9.805132585 + -3.625 = 6.180132585
x = 6.180132585

Simplifying
x = 6.180132585


Subproblem 2
x + 3.625 = -9.805132585

Simplifying
x + 3.625 = -9.805132585

Reorder the terms:
3.625 + x = -9.805132585

Solving
3.625 + x = -9.805132585

Solving for variable 'x'.

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

Add '-3.625' to each side of the equation.
3.625 + -3.625 + x = -9.805132585 + -3.625

Combine like terms: 3.625 + -3.625 = 0.000
0.000 + x = -9.805132585 + -3.625
x = -9.805132585 + -3.625

Combine like terms: -9.805132585 + -3.625 = -13.430132585
x = -13.430132585

Simplifying
x = -13.430132585


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.180132585, -13.430132585}
Solution
x = {6.180132585, -13.430132585}

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