(2x+5)(2x+5)=27

Solution for (2x+5)(2x+5)=27 equation:

Simplifying
(2x + 5)(2x + 5) = 27

Reorder the terms:
(5 + 2x)(2x + 5) = 27

Reorder the terms:
(5 + 2x)(5 + 2x) = 27

Multiply (5 + 2x) * (5 + 2x)
(5(5 + 2x) + 2x * (5 + 2x)) = 27
((5 * 5 + 2x * 5) + 2x * (5 + 2x)) = 27
((25 + 10x) + 2x * (5 + 2x)) = 27
(25 + 10x + (5 * 2x + 2x * 2x)) = 27
(25 + 10x + (10x + 4x2)) = 27

Combine like terms: 10x + 10x = 20x
(25 + 20x + 4x2) = 27

Solving
25 + 20x + 4x2 = 27

Solving for variable 'x'.

Reorder the terms:
25 + -27 + 20x + 4x2 = 27 + -27

Combine like terms: 25 + -27 = -2
-2 + 20x + 4x2 = 27 + -27

Combine like terms: 27 + -27 = 0
-2 + 20x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 10x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + 10x + 2x2)' equal to zero and attempt to solve:

Simplifying
-1 + 10x + 2x2 = 0

Solving
-1 + 10x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-0.5 + 5x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 5x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 5x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 5x + x2 = 0 + 0.5
5x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
5x + x2 = 0.5

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 0.5 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 0.5 + 6.25

Combine like terms: 0.5 + 6.25 = 6.75
6.25 + 5x + x2 = 6.75

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 6.75

Calculate the square root of the right side: 2.598076211

Break this problem into two subproblems by setting 
(x + 2.5) equal to 2.598076211 and -2.598076211.

Subproblem 1
x + 2.5 = 2.598076211

Simplifying
x + 2.5 = 2.598076211

Reorder the terms:
2.5 + x = 2.598076211

Solving
2.5 + x = 2.598076211

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 2.598076211 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 2.598076211 + -2.5
x = 2.598076211 + -2.5

Combine like terms: 2.598076211 + -2.5 = 0.098076211
x = 0.098076211

Simplifying
x = 0.098076211

Subproblem 2
x + 2.5 = -2.598076211

Simplifying
x + 2.5 = -2.598076211

Reorder the terms:
2.5 + x = -2.598076211

Solving
2.5 + x = -2.598076211

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -2.598076211 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -2.598076211 + -2.5
x = -2.598076211 + -2.5

Combine like terms: -2.598076211 + -2.5 = -5.098076211
x = -5.098076211

Simplifying
x = -5.098076211

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.098076211, -5.098076211}
Solution
x = {0.098076211, -5.098076211}