2x^2+32x+28=0

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Solution for 2x^2+32x+28=0 equation: 


Simplifying
2x2 + 32x + 28 = 0

Reorder the terms:
28 + 32x + 2x2 = 0

Solving
28 + 32x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(14 + 16x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(14 + 16x + x2)' equal to zero and attempt to solve:

Simplifying
14 + 16x + x2 = 0

Solving
14 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + 16x + -14 + x2 = 0 + -14

Reorder the terms:
14 + -14 + 16x + x2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + 16x + x2 = 0 + -14
16x + x2 = 0 + -14

Combine like terms: 0 + -14 = -14
16x + x2 = -14

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = -14 + 64

Reorder the terms:
64 + 16x + x2 = -14 + 64

Combine like terms: -14 + 64 = 50
64 + 16x + x2 = 50

Factor a perfect square on the left side:
(x + 8)(x + 8) = 50

Calculate the square root of the right side: 7.071067812

Break this problem into two subproblems by setting 
(x + 8) equal to 7.071067812 and -7.071067812.


Subproblem 1
x + 8 = 7.071067812

Simplifying
x + 8 = 7.071067812

Reorder the terms:
8 + x = 7.071067812

Solving
8 + x = 7.071067812

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = 7.071067812 + -8

Combine like terms: 8 + -8 = 0
0 + x = 7.071067812 + -8
x = 7.071067812 + -8

Combine like terms: 7.071067812 + -8 = -0.928932188
x = -0.928932188

Simplifying
x = -0.928932188


Subproblem 2
x + 8 = -7.071067812

Simplifying
x + 8 = -7.071067812

Reorder the terms:
8 + x = -7.071067812

Solving
8 + x = -7.071067812

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = -7.071067812 + -8

Combine like terms: 8 + -8 = 0
0 + x = -7.071067812 + -8
x = -7.071067812 + -8

Combine like terms: -7.071067812 + -8 = -15.071067812
x = -15.071067812

Simplifying
x = -15.071067812


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.928932188, -15.071067812}
Solution
x = {-0.928932188, -15.071067812}

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