2x^2+64x-28=0

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Solution for 2x^2+64x-28=0 equation: 


Simplifying
2x2 + 64x + -28 = 0

Reorder the terms:
-28 + 64x + 2x2 = 0

Solving
-28 + 64x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + 32x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-14 + 32x + x2)' equal to zero and attempt to solve:

Simplifying
-14 + 32x + x2 = 0

Solving
-14 + 32x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 32x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + 32x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 32x + x2 = 0 + 14
32x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
32x + x2 = 14

The x term is 32x.  Take half its coefficient (16).
Square it (256) and add it to both sides.

Add '256' to each side of the equation.
32x + 256 + x2 = 14 + 256

Reorder the terms:
256 + 32x + x2 = 14 + 256

Combine like terms: 14 + 256 = 270
256 + 32x + x2 = 270

Factor a perfect square on the left side:
(x + 16)(x + 16) = 270

Calculate the square root of the right side: 16.431676725

Break this problem into two subproblems by setting 
(x + 16) equal to 16.431676725 and -16.431676725.


Subproblem 1
x + 16 = 16.431676725

Simplifying
x + 16 = 16.431676725

Reorder the terms:
16 + x = 16.431676725

Solving
16 + x = 16.431676725

Solving for variable 'x'.

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

Add '-16' to each side of the equation.
16 + -16 + x = 16.431676725 + -16

Combine like terms: 16 + -16 = 0
0 + x = 16.431676725 + -16
x = 16.431676725 + -16

Combine like terms: 16.431676725 + -16 = 0.431676725
x = 0.431676725

Simplifying
x = 0.431676725


Subproblem 2
x + 16 = -16.431676725

Simplifying
x + 16 = -16.431676725

Reorder the terms:
16 + x = -16.431676725

Solving
16 + x = -16.431676725

Solving for variable 'x'.

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

Add '-16' to each side of the equation.
16 + -16 + x = -16.431676725 + -16

Combine like terms: 16 + -16 = 0
0 + x = -16.431676725 + -16
x = -16.431676725 + -16

Combine like terms: -16.431676725 + -16 = -32.431676725
x = -32.431676725

Simplifying
x = -32.431676725


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.431676725, -32.431676725}
Solution
x = {0.431676725, -32.431676725}

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