36x^2-4x-16=0

Solution for 36x^2-4x-16=0 equation:

Simplifying
36x2 + -4x + -16 = 0

Reorder the terms:
-16 + -4x + 36x2 = 0

Solving
-16 + -4x + 36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-4 + -1x + 9x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-4 + -1x + 9x2)' equal to zero and attempt to solve:

Simplifying
-4 + -1x + 9x2 = 0

Solving
-4 + -1x + 9x2 = 0

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

Divide each side by '9'.
-0.4444444444 + -0.1111111111x + x2 = 0

Move the constant term to the right:

Add '0.4444444444' to each side of the equation.
-0.4444444444 + -0.1111111111x + 0.4444444444 + x2 = 0 + 0.4444444444

Reorder the terms:
-0.4444444444 + 0.4444444444 + -0.1111111111x + x2 = 0 + 0.4444444444

Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000
0.0000000000 + -0.1111111111x + x2 = 0 + 0.4444444444
-0.1111111111x + x2 = 0 + 0.4444444444

Combine like terms: 0 + 0.4444444444 = 0.4444444444
-0.1111111111x + x2 = 0.4444444444

The x term is -0.1111111111x.  Take half its coefficient (-0.05555555555).
Square it (0.003086419752) and add it to both sides.

Add '0.003086419752' to each side of the equation.
-0.1111111111x + 0.003086419752 + x2 = 0.4444444444 + 0.003086419752

Reorder the terms:
0.003086419752 + -0.1111111111x + x2 = 0.4444444444 + 0.003086419752

Combine like terms: 0.4444444444 + 0.003086419752 = 0.447530864152
0.003086419752 + -0.1111111111x + x2 = 0.447530864152

Factor a perfect square on the left side:
(x + -0.05555555555)(x + -0.05555555555) = 0.447530864152

Calculate the square root of the right side: 0.668977477

Break this problem into two subproblems by setting 
(x + -0.05555555555) equal to 0.668977477 and -0.668977477.

Subproblem 1
x + -0.05555555555 = 0.668977477

Simplifying
x + -0.05555555555 = 0.668977477

Reorder the terms:
-0.05555555555 + x = 0.668977477

Solving
-0.05555555555 + x = 0.668977477

Solving for variable 'x'.

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

Add '0.05555555555' to each side of the equation.
-0.05555555555 + 0.05555555555 + x = 0.668977477 + 0.05555555555

Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000
0.00000000000 + x = 0.668977477 + 0.05555555555
x = 0.668977477 + 0.05555555555

Combine like terms: 0.668977477 + 0.05555555555 = 0.72453303255
x = 0.72453303255

Simplifying
x = 0.72453303255

Subproblem 2
x + -0.05555555555 = -0.668977477

Simplifying
x + -0.05555555555 = -0.668977477

Reorder the terms:
-0.05555555555 + x = -0.668977477

Solving
-0.05555555555 + x = -0.668977477

Solving for variable 'x'.

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

Add '0.05555555555' to each side of the equation.
-0.05555555555 + 0.05555555555 + x = -0.668977477 + 0.05555555555

Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000
0.00000000000 + x = -0.668977477 + 0.05555555555
x = -0.668977477 + 0.05555555555

Combine like terms: -0.668977477 + 0.05555555555 = -0.61342192145
x = -0.61342192145

Simplifying
x = -0.61342192145

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.72453303255, -0.61342192145}
Solution
x = {0.72453303255, -0.61342192145}