6x^2+64x-416=0

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Solution for 6x^2+64x-416=0 equation: 


Simplifying
6x2 + 64x + -416 = 0

Reorder the terms:
-416 + 64x + 6x2 = 0

Solving
-416 + 64x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-208 + 32x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-208 + 32x + 3x2)' equal to zero and attempt to solve:

Simplifying
-208 + 32x + 3x2 = 0

Solving
-208 + 32x + 3x2 = 0

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

Divide each side by '3'.
-69.33333333 + 10.66666667x + x2 = 0

Move the constant term to the right:

Add '69.33333333' to each side of the equation.
-69.33333333 + 10.66666667x + 69.33333333 + x2 = 0 + 69.33333333

Reorder the terms:
-69.33333333 + 69.33333333 + 10.66666667x + x2 = 0 + 69.33333333

Combine like terms: -69.33333333 + 69.33333333 = 0.00000000
0.00000000 + 10.66666667x + x2 = 0 + 69.33333333
10.66666667x + x2 = 0 + 69.33333333

Combine like terms: 0 + 69.33333333 = 69.33333333
10.66666667x + x2 = 69.33333333

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 = 69.33333333 + 28.44444446

Reorder the terms:
28.44444446 + 10.66666667x + x2 = 69.33333333 + 28.44444446

Combine like terms: 69.33333333 + 28.44444446 = 97.77777779
28.44444446 + 10.66666667x + x2 = 97.77777779

Factor a perfect square on the left side:
(x + 5.333333335)(x + 5.333333335) = 97.77777779

Calculate the square root of the right side: 9.88826465

Break this problem into two subproblems by setting 
(x + 5.333333335) equal to 9.88826465 and -9.88826465.


Subproblem 1
x + 5.333333335 = 9.88826465

Simplifying
x + 5.333333335 = 9.88826465

Reorder the terms:
5.333333335 + x = 9.88826465

Solving
5.333333335 + x = 9.88826465

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 = 9.88826465 + -5.333333335

Combine like terms: 5.333333335 + -5.333333335 = 0.000000000
0.000000000 + x = 9.88826465 + -5.333333335
x = 9.88826465 + -5.333333335

Combine like terms: 9.88826465 + -5.333333335 = 4.554931315
x = 4.554931315

Simplifying
x = 4.554931315


Subproblem 2
x + 5.333333335 = -9.88826465

Simplifying
x + 5.333333335 = -9.88826465

Reorder the terms:
5.333333335 + x = -9.88826465

Solving
5.333333335 + x = -9.88826465

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 = -9.88826465 + -5.333333335

Combine like terms: 5.333333335 + -5.333333335 = 0.000000000
0.000000000 + x = -9.88826465 + -5.333333335
x = -9.88826465 + -5.333333335

Combine like terms: -9.88826465 + -5.333333335 = -15.221597985
x = -15.221597985

Simplifying
x = -15.221597985


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.554931315, -15.221597985}
Solution
x = {4.554931315, -15.221597985}

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