4x(6x+2)=88

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Solution for 4x(6x+2)=88 equation: 


Simplifying
4x(6x + 2) = 88

Reorder the terms:
4x(2 + 6x) = 88
(2 * 4x + 6x * 4x) = 88
(8x + 24x2) = 88

Solving
8x + 24x2 = 88

Solving for variable 'x'.

Reorder the terms:
-88 + 8x + 24x2 = 88 + -88

Combine like terms: 88 + -88 = 0
-88 + 8x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-11 + x + 3x2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-11 + x + 3x2)' equal to zero and attempt to solve:

Simplifying
-11 + x + 3x2 = 0

Solving
-11 + x + 3x2 = 0

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

Divide each side by '3'.
-3.666666667 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '3.666666667' to each side of the equation.
-3.666666667 + 0.3333333333x + 3.666666667 + x2 = 0 + 3.666666667

Reorder the terms:
-3.666666667 + 3.666666667 + 0.3333333333x + x2 = 0 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + 0.3333333333x + x2 = 0 + 3.666666667
0.3333333333x + x2 = 0 + 3.666666667

Combine like terms: 0 + 3.666666667 = 3.666666667
0.3333333333x + x2 = 3.666666667

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.3333333333x + 0.25 + x2 = 3.666666667 + 0.25

Reorder the terms:
0.25 + 0.3333333333x + x2 = 3.666666667 + 0.25

Combine like terms: 3.666666667 + 0.25 = 3.916666667
0.25 + 0.3333333333x + x2 = 3.916666667

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 3.916666667

Calculate the square root of the right side: 1.979057015

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.979057015 and -1.979057015.


Subproblem 1
x + 0.5 = 1.979057015

Simplifying
x + 0.5 = 1.979057015

Reorder the terms:
0.5 + x = 1.979057015

Solving
0.5 + x = 1.979057015

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 1.979057015 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.979057015 + -0.5
x = 1.979057015 + -0.5

Combine like terms: 1.979057015 + -0.5 = 1.479057015
x = 1.479057015

Simplifying
x = 1.479057015


Subproblem 2
x + 0.5 = -1.979057015

Simplifying
x + 0.5 = -1.979057015

Reorder the terms:
0.5 + x = -1.979057015

Solving
0.5 + x = -1.979057015

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -1.979057015 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.979057015 + -0.5
x = -1.979057015 + -0.5

Combine like terms: -1.979057015 + -0.5 = -2.479057015
x = -2.479057015

Simplifying
x = -2.479057015


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.479057015, -2.479057015}
Solution
x = {1.479057015, -2.479057015}

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