16x^2-18x-18=6

Solution for 16x^2-18x-18=6 equation:

Simplifying
16x2 + -18x + -18 = 6

Reorder the terms:
-18 + -18x + 16x2 = 6

Solving
-18 + -18x + 16x2 = 6

Solving for variable 'x'.

Reorder the terms:
-18 + -6 + -18x + 16x2 = 6 + -6

Combine like terms: -18 + -6 = -24
-24 + -18x + 16x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-24 + -18x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + -9x + 8x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-12 + -9x + 8x2)' equal to zero and attempt to solve:

Simplifying
-12 + -9x + 8x2 = 0

Solving
-12 + -9x + 8x2 = 0

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

Divide each side by '8'.
-1.5 + -1.125x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -1.125x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -1.125x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -1.125x + x2 = 0 + 1.5
-1.125x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-1.125x + x2 = 1.5

The x term is -1.125x.  Take half its coefficient (-0.5625).
Square it (0.31640625) and add it to both sides.

Add '0.31640625' to each side of the equation.
-1.125x + 0.31640625 + x2 = 1.5 + 0.31640625

Reorder the terms:
0.31640625 + -1.125x + x2 = 1.5 + 0.31640625

Combine like terms: 1.5 + 0.31640625 = 1.81640625
0.31640625 + -1.125x + x2 = 1.81640625

Factor a perfect square on the left side:
(x + -0.5625)(x + -0.5625) = 1.81640625

Calculate the square root of the right side: 1.347741166

Break this problem into two subproblems by setting 
(x + -0.5625) equal to 1.347741166 and -1.347741166.

Subproblem 1
x + -0.5625 = 1.347741166

Simplifying
x + -0.5625 = 1.347741166

Reorder the terms:
-0.5625 + x = 1.347741166

Solving
-0.5625 + x = 1.347741166

Solving for variable 'x'.

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

Add '0.5625' to each side of the equation.
-0.5625 + 0.5625 + x = 1.347741166 + 0.5625

Combine like terms: -0.5625 + 0.5625 = 0.0000
0.0000 + x = 1.347741166 + 0.5625
x = 1.347741166 + 0.5625

Combine like terms: 1.347741166 + 0.5625 = 1.910241166
x = 1.910241166

Simplifying
x = 1.910241166

Subproblem 2
x + -0.5625 = -1.347741166

Simplifying
x + -0.5625 = -1.347741166

Reorder the terms:
-0.5625 + x = -1.347741166

Solving
-0.5625 + x = -1.347741166

Solving for variable 'x'.

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

Add '0.5625' to each side of the equation.
-0.5625 + 0.5625 + x = -1.347741166 + 0.5625

Combine like terms: -0.5625 + 0.5625 = 0.0000
0.0000 + x = -1.347741166 + 0.5625
x = -1.347741166 + 0.5625

Combine like terms: -1.347741166 + 0.5625 = -0.785241166
x = -0.785241166

Simplifying
x = -0.785241166

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.910241166, -0.785241166}
Solution
x = {1.910241166, -0.785241166}