2x(2x+8)=960

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Solution for 2x(2x+8)=960 equation: 


Simplifying
2x(2x + 8) = 960

Reorder the terms:
2x(8 + 2x) = 960
(8 * 2x + 2x * 2x) = 960
(16x + 4x2) = 960

Solving
16x + 4x2 = 960

Solving for variable 'x'.

Reorder the terms:
-960 + 16x + 4x2 = 960 + -960

Combine like terms: 960 + -960 = 0
-960 + 16x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-240 + 4x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-240 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
-240 + 4x + x2 = 0

Solving
-240 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '240' to each side of the equation.
-240 + 4x + 240 + x2 = 0 + 240

Reorder the terms:
-240 + 240 + 4x + x2 = 0 + 240

Combine like terms: -240 + 240 = 0
0 + 4x + x2 = 0 + 240
4x + x2 = 0 + 240

Combine like terms: 0 + 240 = 240
4x + x2 = 240

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 = 240 + 4

Reorder the terms:
4 + 4x + x2 = 240 + 4

Combine like terms: 240 + 4 = 244
4 + 4x + x2 = 244

Factor a perfect square on the left side:
(x + 2)(x + 2) = 244

Calculate the square root of the right side: 15.620499352

Break this problem into two subproblems by setting 
(x + 2) equal to 15.620499352 and -15.620499352.


Subproblem 1
x + 2 = 15.620499352

Simplifying
x + 2 = 15.620499352

Reorder the terms:
2 + x = 15.620499352

Solving
2 + x = 15.620499352

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 = 15.620499352 + -2

Combine like terms: 2 + -2 = 0
0 + x = 15.620499352 + -2
x = 15.620499352 + -2

Combine like terms: 15.620499352 + -2 = 13.620499352
x = 13.620499352

Simplifying
x = 13.620499352


Subproblem 2
x + 2 = -15.620499352

Simplifying
x + 2 = -15.620499352

Reorder the terms:
2 + x = -15.620499352

Solving
2 + x = -15.620499352

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 = -15.620499352 + -2

Combine like terms: 2 + -2 = 0
0 + x = -15.620499352 + -2
x = -15.620499352 + -2

Combine like terms: -15.620499352 + -2 = -17.620499352
x = -17.620499352

Simplifying
x = -17.620499352


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.620499352, -17.620499352}
Solution
x = {13.620499352, -17.620499352}

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