(2x^2)+8x-76=0

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Solution for (2x^2)+8x-76=0 equation: 


Simplifying
(2x2) + 8x + -76 = 0

Reorder the terms:
-76 + 8x + (2x2) = 0

Solving
-76 + 8x + (2x2) = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-38 + 4x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-38 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
-38 + 4x + x2 = 0

Solving
-38 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '38' to each side of the equation.
-38 + 4x + 38 + x2 = 0 + 38

Reorder the terms:
-38 + 38 + 4x + x2 = 0 + 38

Combine like terms: -38 + 38 = 0
0 + 4x + x2 = 0 + 38
4x + x2 = 0 + 38

Combine like terms: 0 + 38 = 38
4x + x2 = 38

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 38 + 4

Reorder the terms:
4 + 4x + x2 = 38 + 4

Combine like terms: 38 + 4 = 42
4 + 4x + x2 = 42

Factor a perfect square on the left side:
(x + 2)(x + 2) = 42

Calculate the square root of the right side: 6.480740698

Break this problem into two subproblems by setting 
(x + 2) equal to 6.480740698 and -6.480740698.


Subproblem 1
x + 2 = 6.480740698

Simplifying
x + 2 = 6.480740698

Reorder the terms:
2 + x = 6.480740698

Solving
2 + x = 6.480740698

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 6.480740698 + -2

Combine like terms: 2 + -2 = 0
0 + x = 6.480740698 + -2
x = 6.480740698 + -2

Combine like terms: 6.480740698 + -2 = 4.480740698
x = 4.480740698

Simplifying
x = 4.480740698


Subproblem 2
x + 2 = -6.480740698

Simplifying
x + 2 = -6.480740698

Reorder the terms:
2 + x = -6.480740698

Solving
2 + x = -6.480740698

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -6.480740698 + -2

Combine like terms: 2 + -2 = 0
0 + x = -6.480740698 + -2
x = -6.480740698 + -2

Combine like terms: -6.480740698 + -2 = -8.480740698
x = -8.480740698

Simplifying
x = -8.480740698


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.480740698, -8.480740698}
Solution
x = {4.480740698, -8.480740698}

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