(2x+3)(2x+3)=13

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Solution for (2x+3)(2x+3)=13 equation: 


Simplifying
(2x + 3)(2x + 3) = 13

Reorder the terms:
(3 + 2x)(2x + 3) = 13

Reorder the terms:
(3 + 2x)(3 + 2x) = 13

Multiply (3 + 2x) * (3 + 2x)
(3(3 + 2x) + 2x * (3 + 2x)) = 13
((3 * 3 + 2x * 3) + 2x * (3 + 2x)) = 13
((9 + 6x) + 2x * (3 + 2x)) = 13
(9 + 6x + (3 * 2x + 2x * 2x)) = 13
(9 + 6x + (6x + 4x2)) = 13

Combine like terms: 6x + 6x = 12x
(9 + 12x + 4x2) = 13

Solving
9 + 12x + 4x2 = 13

Solving for variable 'x'.

Reorder the terms:
9 + -13 + 12x + 4x2 = 13 + -13

Combine like terms: 9 + -13 = -4
-4 + 12x + 4x2 = 13 + -13

Combine like terms: 13 + -13 = 0
-4 + 12x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + 3x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-1 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
-1 + 3x + x2 = 0

Solving
-1 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 3x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 3x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 3x + x2 = 0 + 1
3x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
3x + x2 = 1

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 1 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 1 + 2.25

Combine like terms: 1 + 2.25 = 3.25
2.25 + 3x + x2 = 3.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(x + 1.5) equal to 1.802775638 and -1.802775638.


Subproblem 1
x + 1.5 = 1.802775638

Simplifying
x + 1.5 = 1.802775638

Reorder the terms:
1.5 + x = 1.802775638

Solving
1.5 + x = 1.802775638

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 1.802775638 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 1.802775638 + -1.5
x = 1.802775638 + -1.5

Combine like terms: 1.802775638 + -1.5 = 0.302775638
x = 0.302775638

Simplifying
x = 0.302775638


Subproblem 2
x + 1.5 = -1.802775638

Simplifying
x + 1.5 = -1.802775638

Reorder the terms:
1.5 + x = -1.802775638

Solving
1.5 + x = -1.802775638

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -1.802775638 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -1.802775638 + -1.5
x = -1.802775638 + -1.5

Combine like terms: -1.802775638 + -1.5 = -3.302775638
x = -3.302775638

Simplifying
x = -3.302775638


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.302775638, -3.302775638}
Solution
x = {0.302775638, -3.302775638}

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