6x^2+64x-72=0

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Solution for 6x^2+64x-72=0 equation: 


Simplifying
6x2 + 64x + -72 = 0

Reorder the terms:
-72 + 64x + 6x2 = 0

Solving
-72 + 64x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-36 + 32x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-36 + 32x + 3x2)' equal to zero and attempt to solve:

Simplifying
-36 + 32x + 3x2 = 0

Solving
-36 + 32x + 3x2 = 0

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

Divide each side by '3'.
-12 + 10.66666667x + x2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 10.66666667x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + 10.66666667x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 10.66666667x + x2 = 0 + 12
10.66666667x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
10.66666667x + x2 = 12

The x term is 10.66666667x.  Take half its coefficient (5.333333335).
Square it (28.44444446) and add it to both sides.

Add '28.44444446' to each side of the equation.
10.66666667x + 28.44444446 + x2 = 12 + 28.44444446

Reorder the terms:
28.44444446 + 10.66666667x + x2 = 12 + 28.44444446

Combine like terms: 12 + 28.44444446 = 40.44444446
28.44444446 + 10.66666667x + x2 = 40.44444446

Factor a perfect square on the left side:
(x + 5.333333335)(x + 5.333333335) = 40.44444446

Calculate the square root of the right side: 6.359594677

Break this problem into two subproblems by setting 
(x + 5.333333335) equal to 6.359594677 and -6.359594677.


Subproblem 1
x + 5.333333335 = 6.359594677

Simplifying
x + 5.333333335 = 6.359594677

Reorder the terms:
5.333333335 + x = 6.359594677

Solving
5.333333335 + x = 6.359594677

Solving for variable 'x'.

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

Add '-5.333333335' to each side of the equation.
5.333333335 + -5.333333335 + x = 6.359594677 + -5.333333335

Combine like terms: 5.333333335 + -5.333333335 = 0.000000000
0.000000000 + x = 6.359594677 + -5.333333335
x = 6.359594677 + -5.333333335

Combine like terms: 6.359594677 + -5.333333335 = 1.026261342
x = 1.026261342

Simplifying
x = 1.026261342


Subproblem 2
x + 5.333333335 = -6.359594677

Simplifying
x + 5.333333335 = -6.359594677

Reorder the terms:
5.333333335 + x = -6.359594677

Solving
5.333333335 + x = -6.359594677

Solving for variable 'x'.

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

Add '-5.333333335' to each side of the equation.
5.333333335 + -5.333333335 + x = -6.359594677 + -5.333333335

Combine like terms: 5.333333335 + -5.333333335 = 0.000000000
0.000000000 + x = -6.359594677 + -5.333333335
x = -6.359594677 + -5.333333335

Combine like terms: -6.359594677 + -5.333333335 = -11.692928012
x = -11.692928012

Simplifying
x = -11.692928012


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.026261342, -11.692928012}
Solution
x = {1.026261342, -11.692928012}

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