2x(x+32)=768

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Solution for 2x(x+32)=768 equation: 


Simplifying
2x(x + 32) = 768

Reorder the terms:
2x(32 + x) = 768
(32 * 2x + x * 2x) = 768
(64x + 2x2) = 768

Solving
64x + 2x2 = 768

Solving for variable 'x'.

Reorder the terms:
-768 + 64x + 2x2 = 768 + -768

Combine like terms: 768 + -768 = 0
-768 + 64x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-384 + 32x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-384 + 32x + x2)' equal to zero and attempt to solve:

Simplifying
-384 + 32x + x2 = 0

Solving
-384 + 32x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '384' to each side of the equation.
-384 + 32x + 384 + x2 = 0 + 384

Reorder the terms:
-384 + 384 + 32x + x2 = 0 + 384

Combine like terms: -384 + 384 = 0
0 + 32x + x2 = 0 + 384
32x + x2 = 0 + 384

Combine like terms: 0 + 384 = 384
32x + x2 = 384

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 = 384 + 256

Reorder the terms:
256 + 32x + x2 = 384 + 256

Combine like terms: 384 + 256 = 640
256 + 32x + x2 = 640

Factor a perfect square on the left side:
(x + 16)(x + 16) = 640

Calculate the square root of the right side: 25.298221281

Break this problem into two subproblems by setting 
(x + 16) equal to 25.298221281 and -25.298221281.


Subproblem 1
x + 16 = 25.298221281

Simplifying
x + 16 = 25.298221281

Reorder the terms:
16 + x = 25.298221281

Solving
16 + x = 25.298221281

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 = 25.298221281 + -16

Combine like terms: 16 + -16 = 0
0 + x = 25.298221281 + -16
x = 25.298221281 + -16

Combine like terms: 25.298221281 + -16 = 9.298221281
x = 9.298221281

Simplifying
x = 9.298221281


Subproblem 2
x + 16 = -25.298221281

Simplifying
x + 16 = -25.298221281

Reorder the terms:
16 + x = -25.298221281

Solving
16 + x = -25.298221281

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 = -25.298221281 + -16

Combine like terms: 16 + -16 = 0
0 + x = -25.298221281 + -16
x = -25.298221281 + -16

Combine like terms: -25.298221281 + -16 = -41.298221281
x = -41.298221281

Simplifying
x = -41.298221281


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.298221281, -41.298221281}
Solution
x = {9.298221281, -41.298221281}

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