6x^2-30x-36=56

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Solution for 6x^2-30x-36=56 equation: 


Simplifying
6x2 + -30x + -36 = 56

Reorder the terms:
-36 + -30x + 6x2 = 56

Solving
-36 + -30x + 6x2 = 56

Solving for variable 'x'.

Reorder the terms:
-36 + -56 + -30x + 6x2 = 56 + -56

Combine like terms: -36 + -56 = -92
-92 + -30x + 6x2 = 56 + -56

Combine like terms: 56 + -56 = 0
-92 + -30x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-46 + -15x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-46 + -15x + 3x2)' equal to zero and attempt to solve:

Simplifying
-46 + -15x + 3x2 = 0

Solving
-46 + -15x + 3x2 = 0

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

Divide each side by '3'.
-15.33333333 + -5x + x2 = 0

Move the constant term to the right:

Add '15.33333333' to each side of the equation.
-15.33333333 + -5x + 15.33333333 + x2 = 0 + 15.33333333

Reorder the terms:
-15.33333333 + 15.33333333 + -5x + x2 = 0 + 15.33333333

Combine like terms: -15.33333333 + 15.33333333 = 0.00000000
0.00000000 + -5x + x2 = 0 + 15.33333333
-5x + x2 = 0 + 15.33333333

Combine like terms: 0 + 15.33333333 = 15.33333333
-5x + x2 = 15.33333333

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 15.33333333 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 15.33333333 + 6.25

Combine like terms: 15.33333333 + 6.25 = 21.58333333
6.25 + -5x + x2 = 21.58333333

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 21.58333333

Calculate the square root of the right side: 4.645786621

Break this problem into two subproblems by setting 
(x + -2.5) equal to 4.645786621 and -4.645786621.


Subproblem 1
x + -2.5 = 4.645786621

Simplifying
x + -2.5 = 4.645786621

Reorder the terms:
-2.5 + x = 4.645786621

Solving
-2.5 + x = 4.645786621

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 4.645786621 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 4.645786621 + 2.5
x = 4.645786621 + 2.5

Combine like terms: 4.645786621 + 2.5 = 7.145786621
x = 7.145786621

Simplifying
x = 7.145786621


Subproblem 2
x + -2.5 = -4.645786621

Simplifying
x + -2.5 = -4.645786621

Reorder the terms:
-2.5 + x = -4.645786621

Solving
-2.5 + x = -4.645786621

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -4.645786621 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -4.645786621 + 2.5
x = -4.645786621 + 2.5

Combine like terms: -4.645786621 + 2.5 = -2.145786621
x = -2.145786621

Simplifying
x = -2.145786621


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.145786621, -2.145786621}
Solution
x = {7.145786621, -2.145786621}

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