8x^2+60x+32=0

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Solution for 8x^2+60x+32=0 equation: 


Simplifying
8x2 + 60x + 32 = 0

Reorder the terms:
32 + 60x + 8x2 = 0

Solving
32 + 60x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(8 + 15x + 2x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(8 + 15x + 2x2)' equal to zero and attempt to solve:

Simplifying
8 + 15x + 2x2 = 0

Solving
8 + 15x + 2x2 = 0

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

Divide each side by '2'.
4 + 7.5x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 7.5x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 7.5x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 7.5x + x2 = 0 + -4
7.5x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
7.5x + x2 = -4

The x term is 7.5x.  Take half its coefficient (3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
7.5x + 14.0625 + x2 = -4 + 14.0625

Reorder the terms:
14.0625 + 7.5x + x2 = -4 + 14.0625

Combine like terms: -4 + 14.0625 = 10.0625
14.0625 + 7.5x + x2 = 10.0625

Factor a perfect square on the left side:
(x + 3.75)(x + 3.75) = 10.0625

Calculate the square root of the right side: 3.172144385

Break this problem into two subproblems by setting 
(x + 3.75) equal to 3.172144385 and -3.172144385.


Subproblem 1
x + 3.75 = 3.172144385

Simplifying
x + 3.75 = 3.172144385

Reorder the terms:
3.75 + x = 3.172144385

Solving
3.75 + x = 3.172144385

Solving for variable 'x'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + x = 3.172144385 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = 3.172144385 + -3.75
x = 3.172144385 + -3.75

Combine like terms: 3.172144385 + -3.75 = -0.577855615
x = -0.577855615

Simplifying
x = -0.577855615


Subproblem 2
x + 3.75 = -3.172144385

Simplifying
x + 3.75 = -3.172144385

Reorder the terms:
3.75 + x = -3.172144385

Solving
3.75 + x = -3.172144385

Solving for variable 'x'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + x = -3.172144385 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = -3.172144385 + -3.75
x = -3.172144385 + -3.75

Combine like terms: -3.172144385 + -3.75 = -6.922144385
x = -6.922144385

Simplifying
x = -6.922144385


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.577855615, -6.922144385}
Solution
x = {-0.577855615, -6.922144385}

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