16x^2+4x-152=0

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Solution for 16x^2+4x-152=0 equation: 


Simplifying
16x2 + 4x + -152 = 0

Reorder the terms:
-152 + 4x + 16x2 = 0

Solving
-152 + 4x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-38 + x + 4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-38 + x + 4x2)' equal to zero and attempt to solve:

Simplifying
-38 + x + 4x2 = 0

Solving
-38 + x + 4x2 = 0

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

Divide each side by '4'.
-9.5 + 0.25x + x2 = 0

Move the constant term to the right:

Add '9.5' to each side of the equation.
-9.5 + 0.25x + 9.5 + x2 = 0 + 9.5

Reorder the terms:
-9.5 + 9.5 + 0.25x + x2 = 0 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + 0.25x + x2 = 0 + 9.5
0.25x + x2 = 0 + 9.5

Combine like terms: 0 + 9.5 = 9.5
0.25x + x2 = 9.5

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.
0.25x + 0.25 + x2 = 9.5 + 0.25

Reorder the terms:
0.25 + 0.25x + x2 = 9.5 + 0.25

Combine like terms: 9.5 + 0.25 = 9.75
0.25 + 0.25x + x2 = 9.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 9.75

Calculate the square root of the right side: 3.122498999

Break this problem into two subproblems by setting 
(x + 0.5) equal to 3.122498999 and -3.122498999.


Subproblem 1
x + 0.5 = 3.122498999

Simplifying
x + 0.5 = 3.122498999

Reorder the terms:
0.5 + x = 3.122498999

Solving
0.5 + x = 3.122498999

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 = 3.122498999 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 3.122498999 + -0.5
x = 3.122498999 + -0.5

Combine like terms: 3.122498999 + -0.5 = 2.622498999
x = 2.622498999

Simplifying
x = 2.622498999


Subproblem 2
x + 0.5 = -3.122498999

Simplifying
x + 0.5 = -3.122498999

Reorder the terms:
0.5 + x = -3.122498999

Solving
0.5 + x = -3.122498999

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 = -3.122498999 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -3.122498999 + -0.5
x = -3.122498999 + -0.5

Combine like terms: -3.122498999 + -0.5 = -3.622498999
x = -3.622498999

Simplifying
x = -3.622498999


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.622498999, -3.622498999}
Solution
x = {2.622498999, -3.622498999}

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