2(x+2)(x+2)+5=11

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Solution for 2(x+2)(x+2)+5=11 equation: 


Simplifying
2(x + 2)(x + 2) + 5 = 11

Reorder the terms:
2(2 + x)(x + 2) + 5 = 11

Reorder the terms:
2(2 + x)(2 + x) + 5 = 11

Multiply (2 + x) * (2 + x)
2(2(2 + x) + x(2 + x)) + 5 = 11
2((2 * 2 + x * 2) + x(2 + x)) + 5 = 11
2((4 + 2x) + x(2 + x)) + 5 = 11
2(4 + 2x + (2 * x + x * x)) + 5 = 11
2(4 + 2x + (2x + x2)) + 5 = 11

Combine like terms: 2x + 2x = 4x
2(4 + 4x + x2) + 5 = 11
(4 * 2 + 4x * 2 + x2 * 2) + 5 = 11
(8 + 8x + 2x2) + 5 = 11

Reorder the terms:
8 + 5 + 8x + 2x2 = 11

Combine like terms: 8 + 5 = 13
13 + 8x + 2x2 = 11

Solving
13 + 8x + 2x2 = 11

Solving for variable 'x'.

Reorder the terms:
13 + -11 + 8x + 2x2 = 11 + -11

Combine like terms: 13 + -11 = 2
2 + 8x + 2x2 = 11 + -11

Combine like terms: 11 + -11 = 0
2 + 8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 4x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
1 + 4x + x2 = 0

Solving
1 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 4x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 4x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4x + x2 = 0 + -1
4x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
4x + x2 = -1

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = -1 + 4

Reorder the terms:
4 + 4x + x2 = -1 + 4

Combine like terms: -1 + 4 = 3
4 + 4x + x2 = 3

Factor a perfect square on the left side:
(x + 2)(x + 2) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x + 2) equal to 1.732050808 and -1.732050808.


Subproblem 1
x + 2 = 1.732050808

Simplifying
x + 2 = 1.732050808

Reorder the terms:
2 + x = 1.732050808

Solving
2 + x = 1.732050808

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 1.732050808 + -2

Combine like terms: 2 + -2 = 0
0 + x = 1.732050808 + -2
x = 1.732050808 + -2

Combine like terms: 1.732050808 + -2 = -0.267949192
x = -0.267949192

Simplifying
x = -0.267949192


Subproblem 2
x + 2 = -1.732050808

Simplifying
x + 2 = -1.732050808

Reorder the terms:
2 + x = -1.732050808

Solving
2 + x = -1.732050808

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -1.732050808 + -2

Combine like terms: 2 + -2 = 0
0 + x = -1.732050808 + -2
x = -1.732050808 + -2

Combine like terms: -1.732050808 + -2 = -3.732050808
x = -3.732050808

Simplifying
x = -3.732050808


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.267949192, -3.732050808}
Solution
x = {-0.267949192, -3.732050808}

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