5(x+9)(x+9)=60

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Solution for 5(x+9)(x+9)=60 equation: 


Simplifying
5(x + 9)(x + 9) = 60

Reorder the terms:
5(9 + x)(x + 9) = 60

Reorder the terms:
5(9 + x)(9 + x) = 60

Multiply (9 + x) * (9 + x)
5(9(9 + x) + x(9 + x)) = 60
5((9 * 9 + x * 9) + x(9 + x)) = 60
5((81 + 9x) + x(9 + x)) = 60
5(81 + 9x + (9 * x + x * x)) = 60
5(81 + 9x + (9x + x2)) = 60

Combine like terms: 9x + 9x = 18x
5(81 + 18x + x2) = 60
(81 * 5 + 18x * 5 + x2 * 5) = 60
(405 + 90x + 5x2) = 60

Solving
405 + 90x + 5x2 = 60

Solving for variable 'x'.

Reorder the terms:
405 + -60 + 90x + 5x2 = 60 + -60

Combine like terms: 405 + -60 = 345
345 + 90x + 5x2 = 60 + -60

Combine like terms: 60 + -60 = 0
345 + 90x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(69 + 18x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(69 + 18x + x2)' equal to zero and attempt to solve:

Simplifying
69 + 18x + x2 = 0

Solving
69 + 18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-69' to each side of the equation.
69 + 18x + -69 + x2 = 0 + -69

Reorder the terms:
69 + -69 + 18x + x2 = 0 + -69

Combine like terms: 69 + -69 = 0
0 + 18x + x2 = 0 + -69
18x + x2 = 0 + -69

Combine like terms: 0 + -69 = -69
18x + x2 = -69

The x term is 18x.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18x + 81 + x2 = -69 + 81

Reorder the terms:
81 + 18x + x2 = -69 + 81

Combine like terms: -69 + 81 = 12
81 + 18x + x2 = 12

Factor a perfect square on the left side:
(x + 9)(x + 9) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(x + 9) equal to 3.464101615 and -3.464101615.


Subproblem 1
x + 9 = 3.464101615

Simplifying
x + 9 = 3.464101615

Reorder the terms:
9 + x = 3.464101615

Solving
9 + x = 3.464101615

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = 3.464101615 + -9

Combine like terms: 9 + -9 = 0
0 + x = 3.464101615 + -9
x = 3.464101615 + -9

Combine like terms: 3.464101615 + -9 = -5.535898385
x = -5.535898385

Simplifying
x = -5.535898385


Subproblem 2
x + 9 = -3.464101615

Simplifying
x + 9 = -3.464101615

Reorder the terms:
9 + x = -3.464101615

Solving
9 + x = -3.464101615

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = -3.464101615 + -9

Combine like terms: 9 + -9 = 0
0 + x = -3.464101615 + -9
x = -3.464101615 + -9

Combine like terms: -3.464101615 + -9 = -12.464101615
x = -12.464101615

Simplifying
x = -12.464101615


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-5.535898385, -12.464101615}
Solution
x = {-5.535898385, -12.464101615}

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