2(x^2+4x-260)=0

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Solution for 2(x^2+4x-260)=0 equation: 


Simplifying
2(x2 + 4x + -260) = 0

Reorder the terms:
2(-260 + 4x + x2) = 0
(-260 * 2 + 4x * 2 + x2 * 2) = 0
(-520 + 8x + 2x2) = 0

Solving
-520 + 8x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-260 + 4x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-260 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
-260 + 4x + x2 = 0

Solving
-260 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '260' to each side of the equation.
-260 + 4x + 260 + x2 = 0 + 260

Reorder the terms:
-260 + 260 + 4x + x2 = 0 + 260

Combine like terms: -260 + 260 = 0
0 + 4x + x2 = 0 + 260
4x + x2 = 0 + 260

Combine like terms: 0 + 260 = 260
4x + x2 = 260

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 = 260 + 4

Reorder the terms:
4 + 4x + x2 = 260 + 4

Combine like terms: 260 + 4 = 264
4 + 4x + x2 = 264

Factor a perfect square on the left side:
(x + 2)(x + 2) = 264

Calculate the square root of the right side: 16.248076809

Break this problem into two subproblems by setting 
(x + 2) equal to 16.248076809 and -16.248076809.


Subproblem 1
x + 2 = 16.248076809

Simplifying
x + 2 = 16.248076809

Reorder the terms:
2 + x = 16.248076809

Solving
2 + x = 16.248076809

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 = 16.248076809 + -2

Combine like terms: 2 + -2 = 0
0 + x = 16.248076809 + -2
x = 16.248076809 + -2

Combine like terms: 16.248076809 + -2 = 14.248076809
x = 14.248076809

Simplifying
x = 14.248076809


Subproblem 2
x + 2 = -16.248076809

Simplifying
x + 2 = -16.248076809

Reorder the terms:
2 + x = -16.248076809

Solving
2 + x = -16.248076809

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 = -16.248076809 + -2

Combine like terms: 2 + -2 = 0
0 + x = -16.248076809 + -2
x = -16.248076809 + -2

Combine like terms: -16.248076809 + -2 = -18.248076809
x = -18.248076809

Simplifying
x = -18.248076809


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.248076809, -18.248076809}
Solution
x = {14.248076809, -18.248076809}

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