16x^2+16x-158=0

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Solution for 16x^2+16x-158=0 equation: 


Simplifying
16x2 + 16x + -158 = 0

Reorder the terms:
-158 + 16x + 16x2 = 0

Solving
-158 + 16x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-79 + 8x + 8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-79 + 8x + 8x2)' equal to zero and attempt to solve:

Simplifying
-79 + 8x + 8x2 = 0

Solving
-79 + 8x + 8x2 = 0

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

Divide each side by '8'.
-9.875 + x + x2 = 0

Move the constant term to the right:

Add '9.875' to each side of the equation.
-9.875 + x + 9.875 + x2 = 0 + 9.875

Reorder the terms:
-9.875 + 9.875 + x + x2 = 0 + 9.875

Combine like terms: -9.875 + 9.875 = 0.000
0.000 + x + x2 = 0 + 9.875
x + x2 = 0 + 9.875

Combine like terms: 0 + 9.875 = 9.875
x + x2 = 9.875

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

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 9.875 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 9.875 + 0.25

Combine like terms: 9.875 + 0.25 = 10.125
1.25 + x2 = 10.125

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 10.125

Calculate the square root of the right side: 3.181980515

Break this problem into two subproblems by setting 
(x + 0.5) equal to 3.181980515 and -3.181980515.


Subproblem 1
x + 0.5 = 3.181980515

Simplifying
x + 0.5 = 3.181980515

Reorder the terms:
0.5 + x = 3.181980515

Solving
0.5 + x = 3.181980515

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 3.181980515 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 3.181980515 + -0.5
x = 3.181980515 + -0.5

Combine like terms: 3.181980515 + -0.5 = 2.681980515
x = 2.681980515

Simplifying
x = 2.681980515


Subproblem 2
x + 0.5 = -3.181980515

Simplifying
x + 0.5 = -3.181980515

Reorder the terms:
0.5 + x = -3.181980515

Solving
0.5 + x = -3.181980515

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -3.181980515 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -3.181980515 + -0.5
x = -3.181980515 + -0.5

Combine like terms: -3.181980515 + -0.5 = -3.681980515
x = -3.681980515

Simplifying
x = -3.681980515


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.681980515, -3.681980515}
Solution
x = {2.681980515, -3.681980515}

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