116=4x(2x+6)

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Solution for 116=4x(2x+6) equation: 


Simplifying
116 = 4x(2x + 6)

Reorder the terms:
116 = 4x(6 + 2x)
116 = (6 * 4x + 2x * 4x)
116 = (24x + 8x2)

Solving
116 = 24x + 8x2

Solving for variable 'x'.

Reorder the terms:
116 + -24x + -8x2 = 24x + -24x + 8x2 + -8x2

Combine like terms: 24x + -24x = 0
116 + -24x + -8x2 = 0 + 8x2 + -8x2
116 + -24x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
116 + -24x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(29 + -6x + -2x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(29 + -6x + -2x2)' equal to zero and attempt to solve:

Simplifying
29 + -6x + -2x2 = 0

Solving
29 + -6x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-14.5 + 3x + x2 = 0

Move the constant term to the right:

Add '14.5' to each side of the equation.
-14.5 + 3x + 14.5 + x2 = 0 + 14.5

Reorder the terms:
-14.5 + 14.5 + 3x + x2 = 0 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + 3x + x2 = 0 + 14.5
3x + x2 = 0 + 14.5

Combine like terms: 0 + 14.5 = 14.5
3x + x2 = 14.5

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 14.5 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 14.5 + 2.25

Combine like terms: 14.5 + 2.25 = 16.75
2.25 + 3x + x2 = 16.75

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 16.75

Calculate the square root of the right side: 4.092676386

Break this problem into two subproblems by setting 
(x + 1.5) equal to 4.092676386 and -4.092676386.


Subproblem 1
x + 1.5 = 4.092676386

Simplifying
x + 1.5 = 4.092676386

Reorder the terms:
1.5 + x = 4.092676386

Solving
1.5 + x = 4.092676386

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 4.092676386 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 4.092676386 + -1.5
x = 4.092676386 + -1.5

Combine like terms: 4.092676386 + -1.5 = 2.592676386
x = 2.592676386

Simplifying
x = 2.592676386


Subproblem 2
x + 1.5 = -4.092676386

Simplifying
x + 1.5 = -4.092676386

Reorder the terms:
1.5 + x = -4.092676386

Solving
1.5 + x = -4.092676386

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -4.092676386 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -4.092676386 + -1.5
x = -4.092676386 + -1.5

Combine like terms: -4.092676386 + -1.5 = -5.592676386
x = -5.592676386

Simplifying
x = -5.592676386


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.592676386, -5.592676386}
Solution
x = {2.592676386, -5.592676386}

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