x(x+4)72=180

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Solution for x(x+4)72=180 equation:


Simplifying
x(x + 4) * 72 = 180

Reorder the terms:
x(4 + x) * 72 = 180

Reorder the terms for easier multiplication:
72x(4 + x) = 180
(4 * 72x + x * 72x) = 180
(288x + 72x2) = 180

Solving
288x + 72x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 288x + 72x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 288x + 72x2 = 0

Factor out the Greatest Common Factor (GCF), '36'.
36(-5 + 8x + 2x2) = 0

Ignore the factor 36.

Subproblem 1
Set the factor '(-5 + 8x + 2x2)' equal to zero and attempt to solve:

Simplifying
-5 + 8x + 2x2 = 0

Solving
-5 + 8x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-2.5 + 4x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 4x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 4x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 4x + x2 = 0 + 2.5
4x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
4x + x2 = 2.5

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 2.5 + 4

Reorder the terms:
4 + 4x + x2 = 2.5 + 4

Combine like terms: 2.5 + 4 = 6.5
4 + 4x + x2 = 6.5

Factor a perfect square on the left side:
(x + 2)(x + 2) = 6.5

Calculate the square root of the right side: 2.549509757

Break this problem into two subproblems by setting 
(x + 2) equal to 2.549509757 and -2.549509757.


Subproblem 1
x + 2 = 2.549509757

Simplifying
x + 2 = 2.549509757

Reorder the terms:
2 + x = 2.549509757

Solving
2 + x = 2.549509757

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 2.549509757 + -2

Combine like terms: 2 + -2 = 0
0 + x = 2.549509757 + -2
x = 2.549509757 + -2

Combine like terms: 2.549509757 + -2 = 0.549509757
x = 0.549509757

Simplifying
x = 0.549509757


Subproblem 2
x + 2 = -2.549509757

Simplifying
x + 2 = -2.549509757

Reorder the terms:
2 + x = -2.549509757

Solving
2 + x = -2.549509757

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -2.549509757 + -2

Combine like terms: 2 + -2 = 0
0 + x = -2.549509757 + -2
x = -2.549509757 + -2

Combine like terms: -2.549509757 + -2 = -4.549509757
x = -4.549509757

Simplifying
x = -4.549509757


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.549509757, -4.549509757}
Solution
x = {0.549509757, -4.549509757}

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