8x^2+46x-764=0

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Solution for 8x^2+46x-764=0 equation: 


Simplifying
8x2 + 46x + -764 = 0

Reorder the terms:
-764 + 46x + 8x2 = 0

Solving
-764 + 46x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-382 + 23x + 4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-382 + 23x + 4x2)' equal to zero and attempt to solve:

Simplifying
-382 + 23x + 4x2 = 0

Solving
-382 + 23x + 4x2 = 0

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

Divide each side by '4'.
-95.5 + 5.75x + x2 = 0

Move the constant term to the right:

Add '95.5' to each side of the equation.
-95.5 + 5.75x + 95.5 + x2 = 0 + 95.5

Reorder the terms:
-95.5 + 95.5 + 5.75x + x2 = 0 + 95.5

Combine like terms: -95.5 + 95.5 = 0.0
0.0 + 5.75x + x2 = 0 + 95.5
5.75x + x2 = 0 + 95.5

Combine like terms: 0 + 95.5 = 95.5
5.75x + x2 = 95.5

The x term is 5.75x.  Take half its coefficient (2.875).
Square it (8.265625) and add it to both sides.

Add '8.265625' to each side of the equation.
5.75x + 8.265625 + x2 = 95.5 + 8.265625

Reorder the terms:
8.265625 + 5.75x + x2 = 95.5 + 8.265625

Combine like terms: 95.5 + 8.265625 = 103.765625
8.265625 + 5.75x + x2 = 103.765625

Factor a perfect square on the left side:
(x + 2.875)(x + 2.875) = 103.765625

Calculate the square root of the right side: 10.186541366

Break this problem into two subproblems by setting 
(x + 2.875) equal to 10.186541366 and -10.186541366.


Subproblem 1
x + 2.875 = 10.186541366

Simplifying
x + 2.875 = 10.186541366

Reorder the terms:
2.875 + x = 10.186541366

Solving
2.875 + x = 10.186541366

Solving for variable 'x'.

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

Add '-2.875' to each side of the equation.
2.875 + -2.875 + x = 10.186541366 + -2.875

Combine like terms: 2.875 + -2.875 = 0.000
0.000 + x = 10.186541366 + -2.875
x = 10.186541366 + -2.875

Combine like terms: 10.186541366 + -2.875 = 7.311541366
x = 7.311541366

Simplifying
x = 7.311541366


Subproblem 2
x + 2.875 = -10.186541366

Simplifying
x + 2.875 = -10.186541366

Reorder the terms:
2.875 + x = -10.186541366

Solving
2.875 + x = -10.186541366

Solving for variable 'x'.

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

Add '-2.875' to each side of the equation.
2.875 + -2.875 + x = -10.186541366 + -2.875

Combine like terms: 2.875 + -2.875 = 0.000
0.000 + x = -10.186541366 + -2.875
x = -10.186541366 + -2.875

Combine like terms: -10.186541366 + -2.875 = -13.061541366
x = -13.061541366

Simplifying
x = -13.061541366


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.311541366, -13.061541366}
Solution
x = {7.311541366, -13.061541366}

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