2x^2+64x-72=0

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Solution for 2x^2+64x-72=0 equation: 


Simplifying
2x2 + 64x + -72 = 0

Reorder the terms:
-72 + 64x + 2x2 = 0

Solving
-72 + 64x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-36 + 32x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-36 + 32x + x2)' equal to zero and attempt to solve:

Simplifying
-36 + 32x + x2 = 0

Solving
-36 + 32x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 32x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + 32x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 32x + x2 = 0 + 36
32x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
32x + x2 = 36

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 = 36 + 256

Reorder the terms:
256 + 32x + x2 = 36 + 256

Combine like terms: 36 + 256 = 292
256 + 32x + x2 = 292

Factor a perfect square on the left side:
(x + 16)(x + 16) = 292

Calculate the square root of the right side: 17.088007491

Break this problem into two subproblems by setting 
(x + 16) equal to 17.088007491 and -17.088007491.


Subproblem 1
x + 16 = 17.088007491

Simplifying
x + 16 = 17.088007491

Reorder the terms:
16 + x = 17.088007491

Solving
16 + x = 17.088007491

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 = 17.088007491 + -16

Combine like terms: 16 + -16 = 0
0 + x = 17.088007491 + -16
x = 17.088007491 + -16

Combine like terms: 17.088007491 + -16 = 1.088007491
x = 1.088007491

Simplifying
x = 1.088007491


Subproblem 2
x + 16 = -17.088007491

Simplifying
x + 16 = -17.088007491

Reorder the terms:
16 + x = -17.088007491

Solving
16 + x = -17.088007491

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 = -17.088007491 + -16

Combine like terms: 16 + -16 = 0
0 + x = -17.088007491 + -16
x = -17.088007491 + -16

Combine like terms: -17.088007491 + -16 = -33.088007491
x = -33.088007491

Simplifying
x = -33.088007491


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.088007491, -33.088007491}
Solution
x = {1.088007491, -33.088007491}

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