3(x+5)(x+5)=21

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Solution for 3(x+5)(x+5)=21 equation: 


Simplifying
3(x + 5)(x + 5) = 21

Reorder the terms:
3(5 + x)(x + 5) = 21

Reorder the terms:
3(5 + x)(5 + x) = 21

Multiply (5 + x) * (5 + x)
3(5(5 + x) + x(5 + x)) = 21
3((5 * 5 + x * 5) + x(5 + x)) = 21
3((25 + 5x) + x(5 + x)) = 21
3(25 + 5x + (5 * x + x * x)) = 21
3(25 + 5x + (5x + x2)) = 21

Combine like terms: 5x + 5x = 10x
3(25 + 10x + x2) = 21
(25 * 3 + 10x * 3 + x2 * 3) = 21
(75 + 30x + 3x2) = 21

Solving
75 + 30x + 3x2 = 21

Solving for variable 'x'.

Reorder the terms:
75 + -21 + 30x + 3x2 = 21 + -21

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

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

Factor out the Greatest Common Factor (GCF), '3'.
3(18 + 10x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(18 + 10x + x2)' equal to zero and attempt to solve:

Simplifying
18 + 10x + x2 = 0

Solving
18 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + 10x + -18 + x2 = 0 + -18

Reorder the terms:
18 + -18 + 10x + x2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + 10x + x2 = 0 + -18
10x + x2 = 0 + -18

Combine like terms: 0 + -18 = -18
10x + x2 = -18

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 = -18 + 25

Reorder the terms:
25 + 10x + x2 = -18 + 25

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

Factor a perfect square on the left side:
(x + 5)(x + 5) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x + 5) equal to 2.645751311 and -2.645751311.


Subproblem 1
x + 5 = 2.645751311

Simplifying
x + 5 = 2.645751311

Reorder the terms:
5 + x = 2.645751311

Solving
5 + x = 2.645751311

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 = 2.645751311 + -5

Combine like terms: 5 + -5 = 0
0 + x = 2.645751311 + -5
x = 2.645751311 + -5

Combine like terms: 2.645751311 + -5 = -2.354248689
x = -2.354248689

Simplifying
x = -2.354248689


Subproblem 2
x + 5 = -2.645751311

Simplifying
x + 5 = -2.645751311

Reorder the terms:
5 + x = -2.645751311

Solving
5 + x = -2.645751311

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 = -2.645751311 + -5

Combine like terms: 5 + -5 = 0
0 + x = -2.645751311 + -5
x = -2.645751311 + -5

Combine like terms: -2.645751311 + -5 = -7.645751311
x = -7.645751311

Simplifying
x = -7.645751311


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.354248689, -7.645751311}
Solution
x = {-2.354248689, -7.645751311}

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