3(x+5)(x+5)=54

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Solution for 3(x+5)(x+5)=54 equation: 


Simplifying
3(x + 5)(x + 5) = 54

Reorder the terms:
3(5 + x)(x + 5) = 54

Reorder the terms:
3(5 + x)(5 + x) = 54

Multiply (5 + x) * (5 + x)
3(5(5 + x) + x(5 + x)) = 54
3((5 * 5 + x * 5) + x(5 + x)) = 54
3((25 + 5x) + x(5 + x)) = 54
3(25 + 5x + (5 * x + x * x)) = 54
3(25 + 5x + (5x + x2)) = 54

Combine like terms: 5x + 5x = 10x
3(25 + 10x + x2) = 54
(25 * 3 + 10x * 3 + x2 * 3) = 54
(75 + 30x + 3x2) = 54

Solving
75 + 30x + 3x2 = 54

Solving for variable 'x'.

Reorder the terms:
75 + -54 + 30x + 3x2 = 54 + -54

Combine like terms: 75 + -54 = 21
21 + 30x + 3x2 = 54 + -54

Combine like terms: 54 + -54 = 0
21 + 30x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(7 + 10x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(7 + 10x + x2)' equal to zero and attempt to solve:

Simplifying
7 + 10x + x2 = 0

Solving
7 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 10x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + 10x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 10x + x2 = 0 + -7
10x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
10x + x2 = -7

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = -7 + 25

Reorder the terms:
25 + 10x + x2 = -7 + 25

Combine like terms: -7 + 25 = 18
25 + 10x + x2 = 18

Factor a perfect square on the left side:
(x + 5)(x + 5) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(x + 5) equal to 4.242640687 and -4.242640687.


Subproblem 1
x + 5 = 4.242640687

Simplifying
x + 5 = 4.242640687

Reorder the terms:
5 + x = 4.242640687

Solving
5 + x = 4.242640687

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 4.242640687 + -5

Combine like terms: 5 + -5 = 0
0 + x = 4.242640687 + -5
x = 4.242640687 + -5

Combine like terms: 4.242640687 + -5 = -0.757359313
x = -0.757359313

Simplifying
x = -0.757359313


Subproblem 2
x + 5 = -4.242640687

Simplifying
x + 5 = -4.242640687

Reorder the terms:
5 + x = -4.242640687

Solving
5 + x = -4.242640687

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -4.242640687 + -5

Combine like terms: 5 + -5 = 0
0 + x = -4.242640687 + -5
x = -4.242640687 + -5

Combine like terms: -4.242640687 + -5 = -9.242640687
x = -9.242640687

Simplifying
x = -9.242640687


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.757359313, -9.242640687}
Solution
x = {-0.757359313, -9.242640687}

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