2x(x+96)=180

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Solution for 2x(x+96)=180 equation: 


Simplifying
2x(x + 96) = 180

Reorder the terms:
2x(96 + x) = 180
(96 * 2x + x * 2x) = 180
(192x + 2x2) = 180

Solving
192x + 2x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 192x + 2x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 192x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-90 + 96x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-90 + 96x + x2)' equal to zero and attempt to solve:

Simplifying
-90 + 96x + x2 = 0

Solving
-90 + 96x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + 96x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + 96x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + 96x + x2 = 0 + 90
96x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
96x + x2 = 90

The x term is 96x.  Take half its coefficient (48).
Square it (2304) and add it to both sides.

Add '2304' to each side of the equation.
96x + 2304 + x2 = 90 + 2304

Reorder the terms:
2304 + 96x + x2 = 90 + 2304

Combine like terms: 90 + 2304 = 2394
2304 + 96x + x2 = 2394

Factor a perfect square on the left side:
(x + 48)(x + 48) = 2394

Calculate the square root of the right side: 48.928519291

Break this problem into two subproblems by setting 
(x + 48) equal to 48.928519291 and -48.928519291.


Subproblem 1
x + 48 = 48.928519291

Simplifying
x + 48 = 48.928519291

Reorder the terms:
48 + x = 48.928519291

Solving
48 + x = 48.928519291

Solving for variable 'x'.

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

Add '-48' to each side of the equation.
48 + -48 + x = 48.928519291 + -48

Combine like terms: 48 + -48 = 0
0 + x = 48.928519291 + -48
x = 48.928519291 + -48

Combine like terms: 48.928519291 + -48 = 0.928519291
x = 0.928519291

Simplifying
x = 0.928519291


Subproblem 2
x + 48 = -48.928519291

Simplifying
x + 48 = -48.928519291

Reorder the terms:
48 + x = -48.928519291

Solving
48 + x = -48.928519291

Solving for variable 'x'.

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

Add '-48' to each side of the equation.
48 + -48 + x = -48.928519291 + -48

Combine like terms: 48 + -48 = 0
0 + x = -48.928519291 + -48
x = -48.928519291 + -48

Combine like terms: -48.928519291 + -48 = -96.928519291
x = -96.928519291

Simplifying
x = -96.928519291


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.928519291, -96.928519291}
Solution
x = {0.928519291, -96.928519291}

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