5(x+8)(x+8)=60

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Solution for 5(x+8)(x+8)=60 equation: 


Simplifying
5(x + 8)(x + 8) = 60

Reorder the terms:
5(8 + x)(x + 8) = 60

Reorder the terms:
5(8 + x)(8 + x) = 60

Multiply (8 + x) * (8 + x)
5(8(8 + x) + x(8 + x)) = 60
5((8 * 8 + x * 8) + x(8 + x)) = 60
5((64 + 8x) + x(8 + x)) = 60
5(64 + 8x + (8 * x + x * x)) = 60
5(64 + 8x + (8x + x2)) = 60

Combine like terms: 8x + 8x = 16x
5(64 + 16x + x2) = 60
(64 * 5 + 16x * 5 + x2 * 5) = 60
(320 + 80x + 5x2) = 60

Solving
320 + 80x + 5x2 = 60

Solving for variable 'x'.

Reorder the terms:
320 + -60 + 80x + 5x2 = 60 + -60

Combine like terms: 320 + -60 = 260
260 + 80x + 5x2 = 60 + -60

Combine like terms: 60 + -60 = 0
260 + 80x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(52 + 16x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(52 + 16x + x2)' equal to zero and attempt to solve:

Simplifying
52 + 16x + x2 = 0

Solving
52 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-52' to each side of the equation.
52 + 16x + -52 + x2 = 0 + -52

Reorder the terms:
52 + -52 + 16x + x2 = 0 + -52

Combine like terms: 52 + -52 = 0
0 + 16x + x2 = 0 + -52
16x + x2 = 0 + -52

Combine like terms: 0 + -52 = -52
16x + x2 = -52

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = -52 + 64

Reorder the terms:
64 + 16x + x2 = -52 + 64

Combine like terms: -52 + 64 = 12
64 + 16x + x2 = 12

Factor a perfect square on the left side:
(x + 8)(x + 8) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(x + 8) equal to 3.464101615 and -3.464101615.


Subproblem 1
x + 8 = 3.464101615

Simplifying
x + 8 = 3.464101615

Reorder the terms:
8 + x = 3.464101615

Solving
8 + x = 3.464101615

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = 3.464101615 + -8

Combine like terms: 8 + -8 = 0
0 + x = 3.464101615 + -8
x = 3.464101615 + -8

Combine like terms: 3.464101615 + -8 = -4.535898385
x = -4.535898385

Simplifying
x = -4.535898385


Subproblem 2
x + 8 = -3.464101615

Simplifying
x + 8 = -3.464101615

Reorder the terms:
8 + x = -3.464101615

Solving
8 + x = -3.464101615

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = -3.464101615 + -8

Combine like terms: 8 + -8 = 0
0 + x = -3.464101615 + -8
x = -3.464101615 + -8

Combine like terms: -3.464101615 + -8 = -11.464101615
x = -11.464101615

Simplifying
x = -11.464101615


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-4.535898385, -11.464101615}
Solution
x = {-4.535898385, -11.464101615}

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