-16x^2-8x+156=0

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Solution for -16x^2-8x+156=0 equation: 


Simplifying
-16x2 + -8x + 156 = 0

Reorder the terms:
156 + -8x + -16x2 = 0

Solving
156 + -8x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(39 + -2x + -4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(39 + -2x + -4x2)' equal to zero and attempt to solve:

Simplifying
39 + -2x + -4x2 = 0

Solving
39 + -2x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-9.75 + 0.5x + x2 = 0

Move the constant term to the right:

Add '9.75' to each side of the equation.
-9.75 + 0.5x + 9.75 + x2 = 0 + 9.75

Reorder the terms:
-9.75 + 9.75 + 0.5x + x2 = 0 + 9.75

Combine like terms: -9.75 + 9.75 = 0.00
0.00 + 0.5x + x2 = 0 + 9.75
0.5x + x2 = 0 + 9.75

Combine like terms: 0 + 9.75 = 9.75
0.5x + x2 = 9.75

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 9.75 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 9.75 + 0.0625

Combine like terms: 9.75 + 0.0625 = 9.8125
0.0625 + 0.5x + x2 = 9.8125

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 9.8125

Calculate the square root of the right side: 3.132491022

Break this problem into two subproblems by setting 
(x + 0.25) equal to 3.132491022 and -3.132491022.


Subproblem 1
x + 0.25 = 3.132491022

Simplifying
x + 0.25 = 3.132491022

Reorder the terms:
0.25 + x = 3.132491022

Solving
0.25 + x = 3.132491022

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 3.132491022 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 3.132491022 + -0.25
x = 3.132491022 + -0.25

Combine like terms: 3.132491022 + -0.25 = 2.882491022
x = 2.882491022

Simplifying
x = 2.882491022


Subproblem 2
x + 0.25 = -3.132491022

Simplifying
x + 0.25 = -3.132491022

Reorder the terms:
0.25 + x = -3.132491022

Solving
0.25 + x = -3.132491022

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -3.132491022 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -3.132491022 + -0.25
x = -3.132491022 + -0.25

Combine like terms: -3.132491022 + -0.25 = -3.382491022
x = -3.382491022

Simplifying
x = -3.382491022


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.882491022, -3.382491022}
Solution
x = {2.882491022, -3.382491022}

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