2x(x+4)=96

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Solution for 2x(x+4)=96 equation: 


Simplifying
2x(x + 4) = 96

Reorder the terms:
2x(4 + x) = 96
(4 * 2x + x * 2x) = 96
(8x + 2x2) = 96

Solving
8x + 2x2 = 96

Solving for variable 'x'.

Reorder the terms:
-96 + 8x + 2x2 = 96 + -96

Combine like terms: 96 + -96 = 0
-96 + 8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-48 + 4x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-48 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
-48 + 4x + x2 = 0

Solving
-48 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + 4x + 48 + x2 = 0 + 48

Reorder the terms:
-48 + 48 + 4x + x2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 4x + x2 = 0 + 48
4x + x2 = 0 + 48

Combine like terms: 0 + 48 = 48
4x + x2 = 48

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 = 48 + 4

Reorder the terms:
4 + 4x + x2 = 48 + 4

Combine like terms: 48 + 4 = 52
4 + 4x + x2 = 52

Factor a perfect square on the left side:
(x + 2)(x + 2) = 52

Calculate the square root of the right side: 7.211102551

Break this problem into two subproblems by setting 
(x + 2) equal to 7.211102551 and -7.211102551.


Subproblem 1
x + 2 = 7.211102551

Simplifying
x + 2 = 7.211102551

Reorder the terms:
2 + x = 7.211102551

Solving
2 + x = 7.211102551

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 = 7.211102551 + -2

Combine like terms: 2 + -2 = 0
0 + x = 7.211102551 + -2
x = 7.211102551 + -2

Combine like terms: 7.211102551 + -2 = 5.211102551
x = 5.211102551

Simplifying
x = 5.211102551


Subproblem 2
x + 2 = -7.211102551

Simplifying
x + 2 = -7.211102551

Reorder the terms:
2 + x = -7.211102551

Solving
2 + x = -7.211102551

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 = -7.211102551 + -2

Combine like terms: 2 + -2 = 0
0 + x = -7.211102551 + -2
x = -7.211102551 + -2

Combine like terms: -7.211102551 + -2 = -9.211102551
x = -9.211102551

Simplifying
x = -9.211102551


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.211102551, -9.211102551}
Solution
x = {5.211102551, -9.211102551}

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