2x^2+64x-500=0

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Solution for 2x^2+64x-500=0 equation: 


Simplifying
2x2 + 64x + -500 = 0

Reorder the terms:
-500 + 64x + 2x2 = 0

Solving
-500 + 64x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-250 + 32x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-250 + 32x + x2)' equal to zero and attempt to solve:

Simplifying
-250 + 32x + x2 = 0

Solving
-250 + 32x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '250' to each side of the equation.
-250 + 32x + 250 + x2 = 0 + 250

Reorder the terms:
-250 + 250 + 32x + x2 = 0 + 250

Combine like terms: -250 + 250 = 0
0 + 32x + x2 = 0 + 250
32x + x2 = 0 + 250

Combine like terms: 0 + 250 = 250
32x + x2 = 250

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 = 250 + 256

Reorder the terms:
256 + 32x + x2 = 250 + 256

Combine like terms: 250 + 256 = 506
256 + 32x + x2 = 506

Factor a perfect square on the left side:
(x + 16)(x + 16) = 506

Calculate the square root of the right side: 22.494443758

Break this problem into two subproblems by setting 
(x + 16) equal to 22.494443758 and -22.494443758.


Subproblem 1
x + 16 = 22.494443758

Simplifying
x + 16 = 22.494443758

Reorder the terms:
16 + x = 22.494443758

Solving
16 + x = 22.494443758

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 = 22.494443758 + -16

Combine like terms: 16 + -16 = 0
0 + x = 22.494443758 + -16
x = 22.494443758 + -16

Combine like terms: 22.494443758 + -16 = 6.494443758
x = 6.494443758

Simplifying
x = 6.494443758


Subproblem 2
x + 16 = -22.494443758

Simplifying
x + 16 = -22.494443758

Reorder the terms:
16 + x = -22.494443758

Solving
16 + x = -22.494443758

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 = -22.494443758 + -16

Combine like terms: 16 + -16 = 0
0 + x = -22.494443758 + -16
x = -22.494443758 + -16

Combine like terms: -22.494443758 + -16 = -38.494443758
x = -38.494443758

Simplifying
x = -38.494443758


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.494443758, -38.494443758}
Solution
x = {6.494443758, -38.494443758}

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