6x^2+52x-56=0

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Solution for 6x^2+52x-56=0 equation: 


Simplifying
6x2 + 52x + -56 = 0

Reorder the terms:
-56 + 52x + 6x2 = 0

Solving
-56 + 52x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-28 + 26x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-28 + 26x + 3x2)' equal to zero and attempt to solve:

Simplifying
-28 + 26x + 3x2 = 0

Solving
-28 + 26x + 3x2 = 0

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

Divide each side by '3'.
-9.333333333 + 8.666666667x + x2 = 0

Move the constant term to the right:

Add '9.333333333' to each side of the equation.
-9.333333333 + 8.666666667x + 9.333333333 + x2 = 0 + 9.333333333

Reorder the terms:
-9.333333333 + 9.333333333 + 8.666666667x + x2 = 0 + 9.333333333

Combine like terms: -9.333333333 + 9.333333333 = 0.000000000
0.000000000 + 8.666666667x + x2 = 0 + 9.333333333
8.666666667x + x2 = 0 + 9.333333333

Combine like terms: 0 + 9.333333333 = 9.333333333
8.666666667x + x2 = 9.333333333

The x term is 8.666666667x.  Take half its coefficient (4.333333334).
Square it (18.77777778) and add it to both sides.

Add '18.77777778' to each side of the equation.
8.666666667x + 18.77777778 + x2 = 9.333333333 + 18.77777778

Reorder the terms:
18.77777778 + 8.666666667x + x2 = 9.333333333 + 18.77777778

Combine like terms: 9.333333333 + 18.77777778 = 28.111111113
18.77777778 + 8.666666667x + x2 = 28.111111113

Factor a perfect square on the left side:
(x + 4.333333334)(x + 4.333333334) = 28.111111113

Calculate the square root of the right side: 5.30199124

Break this problem into two subproblems by setting 
(x + 4.333333334) equal to 5.30199124 and -5.30199124.


Subproblem 1
x + 4.333333334 = 5.30199124

Simplifying
x + 4.333333334 = 5.30199124

Reorder the terms:
4.333333334 + x = 5.30199124

Solving
4.333333334 + x = 5.30199124

Solving for variable 'x'.

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

Add '-4.333333334' to each side of the equation.
4.333333334 + -4.333333334 + x = 5.30199124 + -4.333333334

Combine like terms: 4.333333334 + -4.333333334 = 0.000000000
0.000000000 + x = 5.30199124 + -4.333333334
x = 5.30199124 + -4.333333334

Combine like terms: 5.30199124 + -4.333333334 = 0.968657906
x = 0.968657906

Simplifying
x = 0.968657906


Subproblem 2
x + 4.333333334 = -5.30199124

Simplifying
x + 4.333333334 = -5.30199124

Reorder the terms:
4.333333334 + x = -5.30199124

Solving
4.333333334 + x = -5.30199124

Solving for variable 'x'.

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

Add '-4.333333334' to each side of the equation.
4.333333334 + -4.333333334 + x = -5.30199124 + -4.333333334

Combine like terms: 4.333333334 + -4.333333334 = 0.000000000
0.000000000 + x = -5.30199124 + -4.333333334
x = -5.30199124 + -4.333333334

Combine like terms: -5.30199124 + -4.333333334 = -9.635324574
x = -9.635324574

Simplifying
x = -9.635324574


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.968657906, -9.635324574}
Solution
x = {0.968657906, -9.635324574}

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