2x^2-8x-308=0

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Solution for 2x^2-8x-308=0 equation: 


Simplifying
2x2 + -8x + -308 = 0

Reorder the terms:
-308 + -8x + 2x2 = 0

Solving
-308 + -8x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-154 + -4x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-154 + -4x + x2)' equal to zero and attempt to solve:

Simplifying
-154 + -4x + x2 = 0

Solving
-154 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '154' to each side of the equation.
-154 + -4x + 154 + x2 = 0 + 154

Reorder the terms:
-154 + 154 + -4x + x2 = 0 + 154

Combine like terms: -154 + 154 = 0
0 + -4x + x2 = 0 + 154
-4x + x2 = 0 + 154

Combine like terms: 0 + 154 = 154
-4x + x2 = 154

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 = 154 + 4

Reorder the terms:
4 + -4x + x2 = 154 + 4

Combine like terms: 154 + 4 = 158
4 + -4x + x2 = 158

Factor a perfect square on the left side:
(x + -2)(x + -2) = 158

Calculate the square root of the right side: 12.56980509

Break this problem into two subproblems by setting 
(x + -2) equal to 12.56980509 and -12.56980509.


Subproblem 1
x + -2 = 12.56980509

Simplifying
x + -2 = 12.56980509

Reorder the terms:
-2 + x = 12.56980509

Solving
-2 + x = 12.56980509

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 = 12.56980509 + 2

Combine like terms: -2 + 2 = 0
0 + x = 12.56980509 + 2
x = 12.56980509 + 2

Combine like terms: 12.56980509 + 2 = 14.56980509
x = 14.56980509

Simplifying
x = 14.56980509


Subproblem 2
x + -2 = -12.56980509

Simplifying
x + -2 = -12.56980509

Reorder the terms:
-2 + x = -12.56980509

Solving
-2 + x = -12.56980509

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 = -12.56980509 + 2

Combine like terms: -2 + 2 = 0
0 + x = -12.56980509 + 2
x = -12.56980509 + 2

Combine like terms: -12.56980509 + 2 = -10.56980509
x = -10.56980509

Simplifying
x = -10.56980509


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.56980509, -10.56980509}
Solution
x = {14.56980509, -10.56980509}

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