2x^2+32x-16=0

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


Simplifying
2x2 + 32x + -16 = 0

Reorder the terms:
-16 + 32x + 2x2 = 0

Solving
-16 + 32x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + 16x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-8 + 16x + x2)' equal to zero and attempt to solve:

Simplifying
-8 + 16x + x2 = 0

Solving
-8 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 16x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 16x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 16x + x2 = 0 + 8
16x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
16x + x2 = 8

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 = 8 + 64

Reorder the terms:
64 + 16x + x2 = 8 + 64

Combine like terms: 8 + 64 = 72
64 + 16x + x2 = 72

Factor a perfect square on the left side:
(x + 8)(x + 8) = 72

Calculate the square root of the right side: 8.485281374

Break this problem into two subproblems by setting 
(x + 8) equal to 8.485281374 and -8.485281374.


Subproblem 1
x + 8 = 8.485281374

Simplifying
x + 8 = 8.485281374

Reorder the terms:
8 + x = 8.485281374

Solving
8 + x = 8.485281374

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 = 8.485281374 + -8

Combine like terms: 8 + -8 = 0
0 + x = 8.485281374 + -8
x = 8.485281374 + -8

Combine like terms: 8.485281374 + -8 = 0.485281374
x = 0.485281374

Simplifying
x = 0.485281374


Subproblem 2
x + 8 = -8.485281374

Simplifying
x + 8 = -8.485281374

Reorder the terms:
8 + x = -8.485281374

Solving
8 + x = -8.485281374

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 = -8.485281374 + -8

Combine like terms: 8 + -8 = 0
0 + x = -8.485281374 + -8
x = -8.485281374 + -8

Combine like terms: -8.485281374 + -8 = -16.485281374
x = -16.485281374

Simplifying
x = -16.485281374


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.485281374, -16.485281374}
Solution
x = {0.485281374, -16.485281374}

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