2x^2+8x-390=0

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Solution for 2x^2+8x-390=0 equation: 


Simplifying
2x2 + 8x + -390 = 0

Reorder the terms:
-390 + 8x + 2x2 = 0

Solving
-390 + 8x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-195 + 4x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-195 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
-195 + 4x + x2 = 0

Solving
-195 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '195' to each side of the equation.
-195 + 4x + 195 + x2 = 0 + 195

Reorder the terms:
-195 + 195 + 4x + x2 = 0 + 195

Combine like terms: -195 + 195 = 0
0 + 4x + x2 = 0 + 195
4x + x2 = 0 + 195

Combine like terms: 0 + 195 = 195
4x + x2 = 195

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 = 195 + 4

Reorder the terms:
4 + 4x + x2 = 195 + 4

Combine like terms: 195 + 4 = 199
4 + 4x + x2 = 199

Factor a perfect square on the left side:
(x + 2)(x + 2) = 199

Calculate the square root of the right side: 14.10673598

Break this problem into two subproblems by setting 
(x + 2) equal to 14.10673598 and -14.10673598.


Subproblem 1
x + 2 = 14.10673598

Simplifying
x + 2 = 14.10673598

Reorder the terms:
2 + x = 14.10673598

Solving
2 + x = 14.10673598

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 = 14.10673598 + -2

Combine like terms: 2 + -2 = 0
0 + x = 14.10673598 + -2
x = 14.10673598 + -2

Combine like terms: 14.10673598 + -2 = 12.10673598
x = 12.10673598

Simplifying
x = 12.10673598


Subproblem 2
x + 2 = -14.10673598

Simplifying
x + 2 = -14.10673598

Reorder the terms:
2 + x = -14.10673598

Solving
2 + x = -14.10673598

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 = -14.10673598 + -2

Combine like terms: 2 + -2 = 0
0 + x = -14.10673598 + -2
x = -14.10673598 + -2

Combine like terms: -14.10673598 + -2 = -16.10673598
x = -16.10673598

Simplifying
x = -16.10673598


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.10673598, -16.10673598}
Solution
x = {12.10673598, -16.10673598}

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