(x+96)5x=180

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Solution for (x+96)5x=180 equation: 


Simplifying
(x + 96) * 5x = 180

Reorder the terms:
(96 + x) * 5x = 180

Reorder the terms for easier multiplication:
5x(96 + x) = 180
(96 * 5x + x * 5x) = 180
(480x + 5x2) = 180

Solving
480x + 5x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 480x + 5x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 480x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-36 + 96x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-36 + 96x + x2)' equal to zero and attempt to solve:

Simplifying
-36 + 96x + x2 = 0

Solving
-36 + 96x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 96x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + 96x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 96x + x2 = 0 + 36
96x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
96x + x2 = 36

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 = 36 + 2304

Reorder the terms:
2304 + 96x + x2 = 36 + 2304

Combine like terms: 36 + 2304 = 2340
2304 + 96x + x2 = 2340

Factor a perfect square on the left side:
(x + 48)(x + 48) = 2340

Calculate the square root of the right side: 48.37354649

Break this problem into two subproblems by setting 
(x + 48) equal to 48.37354649 and -48.37354649.


Subproblem 1
x + 48 = 48.37354649

Simplifying
x + 48 = 48.37354649

Reorder the terms:
48 + x = 48.37354649

Solving
48 + x = 48.37354649

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 = 48.37354649 + -48

Combine like terms: 48 + -48 = 0
0 + x = 48.37354649 + -48
x = 48.37354649 + -48

Combine like terms: 48.37354649 + -48 = 0.37354649
x = 0.37354649

Simplifying
x = 0.37354649


Subproblem 2
x + 48 = -48.37354649

Simplifying
x + 48 = -48.37354649

Reorder the terms:
48 + x = -48.37354649

Solving
48 + x = -48.37354649

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 = -48.37354649 + -48

Combine like terms: 48 + -48 = 0
0 + x = -48.37354649 + -48
x = -48.37354649 + -48

Combine like terms: -48.37354649 + -48 = -96.37354649
x = -96.37354649

Simplifying
x = -96.37354649


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.37354649, -96.37354649}
Solution
x = {0.37354649, -96.37354649}

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