6x^2-12x-90=10

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Solution for 6x^2-12x-90=10 equation: 


Simplifying
6x2 + -12x + -90 = 10

Reorder the terms:
-90 + -12x + 6x2 = 10

Solving
-90 + -12x + 6x2 = 10

Solving for variable 'x'.

Reorder the terms:
-90 + -10 + -12x + 6x2 = 10 + -10

Combine like terms: -90 + -10 = -100
-100 + -12x + 6x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-100 + -12x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-50 + -6x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-50 + -6x + 3x2)' equal to zero and attempt to solve:

Simplifying
-50 + -6x + 3x2 = 0

Solving
-50 + -6x + 3x2 = 0

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

Divide each side by '3'.
-16.66666667 + -2x + x2 = 0

Move the constant term to the right:

Add '16.66666667' to each side of the equation.
-16.66666667 + -2x + 16.66666667 + x2 = 0 + 16.66666667

Reorder the terms:
-16.66666667 + 16.66666667 + -2x + x2 = 0 + 16.66666667

Combine like terms: -16.66666667 + 16.66666667 = 0.00000000
0.00000000 + -2x + x2 = 0 + 16.66666667
-2x + x2 = 0 + 16.66666667

Combine like terms: 0 + 16.66666667 = 16.66666667
-2x + x2 = 16.66666667

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 16.66666667 + 1

Reorder the terms:
1 + -2x + x2 = 16.66666667 + 1

Combine like terms: 16.66666667 + 1 = 17.66666667
1 + -2x + x2 = 17.66666667

Factor a perfect square on the left side:
(x + -1)(x + -1) = 17.66666667

Calculate the square root of the right side: 4.203173405

Break this problem into two subproblems by setting 
(x + -1) equal to 4.203173405 and -4.203173405.


Subproblem 1
x + -1 = 4.203173405

Simplifying
x + -1 = 4.203173405

Reorder the terms:
-1 + x = 4.203173405

Solving
-1 + x = 4.203173405

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 4.203173405 + 1

Combine like terms: -1 + 1 = 0
0 + x = 4.203173405 + 1
x = 4.203173405 + 1

Combine like terms: 4.203173405 + 1 = 5.203173405
x = 5.203173405

Simplifying
x = 5.203173405


Subproblem 2
x + -1 = -4.203173405

Simplifying
x + -1 = -4.203173405

Reorder the terms:
-1 + x = -4.203173405

Solving
-1 + x = -4.203173405

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -4.203173405 + 1

Combine like terms: -1 + 1 = 0
0 + x = -4.203173405 + 1
x = -4.203173405 + 1

Combine like terms: -4.203173405 + 1 = -3.203173405
x = -3.203173405

Simplifying
x = -3.203173405


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.203173405, -3.203173405}
Solution
x = {5.203173405, -3.203173405}

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