-16x^2-8x+68=0

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Solution for -16x^2-8x+68=0 equation: 


Simplifying
-16x2 + -8x + 68 = 0

Reorder the terms:
68 + -8x + -16x2 = 0

Solving
68 + -8x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(17 + -2x + -4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(17 + -2x + -4x2)' equal to zero and attempt to solve:

Simplifying
17 + -2x + -4x2 = 0

Solving
17 + -2x + -4x2 = 0

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

Divide each side by '-4'.
-4.25 + 0.5x + x2 = 0

Move the constant term to the right:

Add '4.25' to each side of the equation.
-4.25 + 0.5x + 4.25 + x2 = 0 + 4.25

Reorder the terms:
-4.25 + 4.25 + 0.5x + x2 = 0 + 4.25

Combine like terms: -4.25 + 4.25 = 0.00
0.00 + 0.5x + x2 = 0 + 4.25
0.5x + x2 = 0 + 4.25

Combine like terms: 0 + 4.25 = 4.25
0.5x + x2 = 4.25

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 = 4.25 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 4.25 + 0.0625

Combine like terms: 4.25 + 0.0625 = 4.3125
0.0625 + 0.5x + x2 = 4.3125

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 4.3125

Calculate the square root of the right side: 2.076655966

Break this problem into two subproblems by setting 
(x + 0.25) equal to 2.076655966 and -2.076655966.


Subproblem 1
x + 0.25 = 2.076655966

Simplifying
x + 0.25 = 2.076655966

Reorder the terms:
0.25 + x = 2.076655966

Solving
0.25 + x = 2.076655966

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 = 2.076655966 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 2.076655966 + -0.25
x = 2.076655966 + -0.25

Combine like terms: 2.076655966 + -0.25 = 1.826655966
x = 1.826655966

Simplifying
x = 1.826655966


Subproblem 2
x + 0.25 = -2.076655966

Simplifying
x + 0.25 = -2.076655966

Reorder the terms:
0.25 + x = -2.076655966

Solving
0.25 + x = -2.076655966

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 = -2.076655966 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -2.076655966 + -0.25
x = -2.076655966 + -0.25

Combine like terms: -2.076655966 + -0.25 = -2.326655966
x = -2.326655966

Simplifying
x = -2.326655966


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.826655966, -2.326655966}
Solution
x = {1.826655966, -2.326655966}

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