3(x+13)(x+13)=54

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Solution for 3(x+13)(x+13)=54 equation: 


Simplifying
3(x + 13)(x + 13) = 54

Reorder the terms:
3(13 + x)(x + 13) = 54

Reorder the terms:
3(13 + x)(13 + x) = 54

Multiply (13 + x) * (13 + x)
3(13(13 + x) + x(13 + x)) = 54
3((13 * 13 + x * 13) + x(13 + x)) = 54
3((169 + 13x) + x(13 + x)) = 54
3(169 + 13x + (13 * x + x * x)) = 54
3(169 + 13x + (13x + x2)) = 54

Combine like terms: 13x + 13x = 26x
3(169 + 26x + x2) = 54
(169 * 3 + 26x * 3 + x2 * 3) = 54
(507 + 78x + 3x2) = 54

Solving
507 + 78x + 3x2 = 54

Solving for variable 'x'.

Reorder the terms:
507 + -54 + 78x + 3x2 = 54 + -54

Combine like terms: 507 + -54 = 453
453 + 78x + 3x2 = 54 + -54

Combine like terms: 54 + -54 = 0
453 + 78x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(151 + 26x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(151 + 26x + x2)' equal to zero and attempt to solve:

Simplifying
151 + 26x + x2 = 0

Solving
151 + 26x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-151' to each side of the equation.
151 + 26x + -151 + x2 = 0 + -151

Reorder the terms:
151 + -151 + 26x + x2 = 0 + -151

Combine like terms: 151 + -151 = 0
0 + 26x + x2 = 0 + -151
26x + x2 = 0 + -151

Combine like terms: 0 + -151 = -151
26x + x2 = -151

The x term is 26x.  Take half its coefficient (13).
Square it (169) and add it to both sides.

Add '169' to each side of the equation.
26x + 169 + x2 = -151 + 169

Reorder the terms:
169 + 26x + x2 = -151 + 169

Combine like terms: -151 + 169 = 18
169 + 26x + x2 = 18

Factor a perfect square on the left side:
(x + 13)(x + 13) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(x + 13) equal to 4.242640687 and -4.242640687.


Subproblem 1
x + 13 = 4.242640687

Simplifying
x + 13 = 4.242640687

Reorder the terms:
13 + x = 4.242640687

Solving
13 + x = 4.242640687

Solving for variable 'x'.

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

Add '-13' to each side of the equation.
13 + -13 + x = 4.242640687 + -13

Combine like terms: 13 + -13 = 0
0 + x = 4.242640687 + -13
x = 4.242640687 + -13

Combine like terms: 4.242640687 + -13 = -8.757359313
x = -8.757359313

Simplifying
x = -8.757359313


Subproblem 2
x + 13 = -4.242640687

Simplifying
x + 13 = -4.242640687

Reorder the terms:
13 + x = -4.242640687

Solving
13 + x = -4.242640687

Solving for variable 'x'.

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

Add '-13' to each side of the equation.
13 + -13 + x = -4.242640687 + -13

Combine like terms: 13 + -13 = 0
0 + x = -4.242640687 + -13
x = -4.242640687 + -13

Combine like terms: -4.242640687 + -13 = -17.242640687
x = -17.242640687

Simplifying
x = -17.242640687


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-8.757359313, -17.242640687}
Solution
x = {-8.757359313, -17.242640687}

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