6x^2-12x-90=34

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Solution for 6x^2-12x-90=34 equation: 


Simplifying
6x2 + -12x + -90 = 34

Reorder the terms:
-90 + -12x + 6x2 = 34

Solving
-90 + -12x + 6x2 = 34

Solving for variable 'x'.

Reorder the terms:
-90 + -34 + -12x + 6x2 = 34 + -34

Combine like terms: -90 + -34 = -124
-124 + -12x + 6x2 = 34 + -34

Combine like terms: 34 + -34 = 0
-124 + -12x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-62 + -6x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-62 + -6x + 3x2)' equal to zero and attempt to solve:

Simplifying
-62 + -6x + 3x2 = 0

Solving
-62 + -6x + 3x2 = 0

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

Divide each side by '3'.
-20.66666667 + -2x + x2 = 0

Move the constant term to the right:

Add '20.66666667' to each side of the equation.
-20.66666667 + -2x + 20.66666667 + x2 = 0 + 20.66666667

Reorder the terms:
-20.66666667 + 20.66666667 + -2x + x2 = 0 + 20.66666667

Combine like terms: -20.66666667 + 20.66666667 = 0.00000000
0.00000000 + -2x + x2 = 0 + 20.66666667
-2x + x2 = 0 + 20.66666667

Combine like terms: 0 + 20.66666667 = 20.66666667
-2x + x2 = 20.66666667

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 = 20.66666667 + 1

Reorder the terms:
1 + -2x + x2 = 20.66666667 + 1

Combine like terms: 20.66666667 + 1 = 21.66666667
1 + -2x + x2 = 21.66666667

Factor a perfect square on the left side:
(x + -1)(x + -1) = 21.66666667

Calculate the square root of the right side: 4.654746682

Break this problem into two subproblems by setting 
(x + -1) equal to 4.654746682 and -4.654746682.


Subproblem 1
x + -1 = 4.654746682

Simplifying
x + -1 = 4.654746682

Reorder the terms:
-1 + x = 4.654746682

Solving
-1 + x = 4.654746682

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 = 4.654746682 + 1

Combine like terms: -1 + 1 = 0
0 + x = 4.654746682 + 1
x = 4.654746682 + 1

Combine like terms: 4.654746682 + 1 = 5.654746682
x = 5.654746682

Simplifying
x = 5.654746682


Subproblem 2
x + -1 = -4.654746682

Simplifying
x + -1 = -4.654746682

Reorder the terms:
-1 + x = -4.654746682

Solving
-1 + x = -4.654746682

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 = -4.654746682 + 1

Combine like terms: -1 + 1 = 0
0 + x = -4.654746682 + 1
x = -4.654746682 + 1

Combine like terms: -4.654746682 + 1 = -3.654746682
x = -3.654746682

Simplifying
x = -3.654746682


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.654746682, -3.654746682}
Solution
x = {5.654746682, -3.654746682}

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