16x^2+124x+32=0

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Solution for 16x^2+124x+32=0 equation: 


Simplifying
16x2 + 124x + 32 = 0

Reorder the terms:
32 + 124x + 16x2 = 0

Solving
32 + 124x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(8 + 31x + 4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(8 + 31x + 4x2)' equal to zero and attempt to solve:

Simplifying
8 + 31x + 4x2 = 0

Solving
8 + 31x + 4x2 = 0

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

Divide each side by '4'.
2 + 7.75x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 7.75x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 7.75x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 7.75x + x2 = 0 + -2
7.75x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
7.75x + x2 = -2

The x term is 7.75x.  Take half its coefficient (3.875).
Square it (15.015625) and add it to both sides.

Add '15.015625' to each side of the equation.
7.75x + 15.015625 + x2 = -2 + 15.015625

Reorder the terms:
15.015625 + 7.75x + x2 = -2 + 15.015625

Combine like terms: -2 + 15.015625 = 13.015625
15.015625 + 7.75x + x2 = 13.015625

Factor a perfect square on the left side:
(x + 3.875)(x + 3.875) = 13.015625

Calculate the square root of the right side: 3.607717422

Break this problem into two subproblems by setting 
(x + 3.875) equal to 3.607717422 and -3.607717422.


Subproblem 1
x + 3.875 = 3.607717422

Simplifying
x + 3.875 = 3.607717422

Reorder the terms:
3.875 + x = 3.607717422

Solving
3.875 + x = 3.607717422

Solving for variable 'x'.

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

Add '-3.875' to each side of the equation.
3.875 + -3.875 + x = 3.607717422 + -3.875

Combine like terms: 3.875 + -3.875 = 0.000
0.000 + x = 3.607717422 + -3.875
x = 3.607717422 + -3.875

Combine like terms: 3.607717422 + -3.875 = -0.267282578
x = -0.267282578

Simplifying
x = -0.267282578


Subproblem 2
x + 3.875 = -3.607717422

Simplifying
x + 3.875 = -3.607717422

Reorder the terms:
3.875 + x = -3.607717422

Solving
3.875 + x = -3.607717422

Solving for variable 'x'.

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

Add '-3.875' to each side of the equation.
3.875 + -3.875 + x = -3.607717422 + -3.875

Combine like terms: 3.875 + -3.875 = 0.000
0.000 + x = -3.607717422 + -3.875
x = -3.607717422 + -3.875

Combine like terms: -3.607717422 + -3.875 = -7.482717422
x = -7.482717422

Simplifying
x = -7.482717422


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.267282578, -7.482717422}
Solution
x = {-0.267282578, -7.482717422}

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