2[(x+4)(x+4)]=22

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Solution for 2[(x+4)(x+4)]=22 equation: 


Simplifying
2[(x + 4)(x + 4)] = 22

Reorder the terms:
2[(4 + x)(x + 4)] = 22

Reorder the terms:
2[(4 + x)(4 + x)] = 22

Multiply (4 + x) * (4 + x)
2[(4(4 + x) + x(4 + x))] = 22
2[((4 * 4 + x * 4) + x(4 + x))] = 22
2[((16 + 4x) + x(4 + x))] = 22
2[(16 + 4x + (4 * x + x * x))] = 22
2[(16 + 4x + (4x + x2))] = 22

Combine like terms: 4x + 4x = 8x
2[(16 + 8x + x2)] = 22
[16 * 2 + 8x * 2 + x2 * 2] = 22
[32 + 16x + 2x2] = 22

Solving
32 + 16x + 2x2 = 22

Solving for variable 'x'.

Reorder the terms:
32 + -22 + 16x + 2x2 = 22 + -22

Combine like terms: 32 + -22 = 10
10 + 16x + 2x2 = 22 + -22

Combine like terms: 22 + -22 = 0
10 + 16x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 8x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + 8x + x2)' equal to zero and attempt to solve:

Simplifying
5 + 8x + x2 = 0

Solving
5 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 8x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + 8x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 8x + x2 = 0 + -5
8x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
8x + x2 = -5

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = -5 + 16

Reorder the terms:
16 + 8x + x2 = -5 + 16

Combine like terms: -5 + 16 = 11
16 + 8x + x2 = 11

Factor a perfect square on the left side:
(x + 4)(x + 4) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + 4) equal to 3.31662479 and -3.31662479.


Subproblem 1
x + 4 = 3.31662479

Simplifying
x + 4 = 3.31662479

Reorder the terms:
4 + x = 3.31662479

Solving
4 + x = 3.31662479

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 3.31662479 + -4

Combine like terms: 4 + -4 = 0
0 + x = 3.31662479 + -4
x = 3.31662479 + -4

Combine like terms: 3.31662479 + -4 = -0.68337521
x = -0.68337521

Simplifying
x = -0.68337521


Subproblem 2
x + 4 = -3.31662479

Simplifying
x + 4 = -3.31662479

Reorder the terms:
4 + x = -3.31662479

Solving
4 + x = -3.31662479

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -3.31662479 + -4

Combine like terms: 4 + -4 = 0
0 + x = -3.31662479 + -4
x = -3.31662479 + -4

Combine like terms: -3.31662479 + -4 = -7.31662479
x = -7.31662479

Simplifying
x = -7.31662479


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.68337521, -7.31662479}
Solution
x = {-0.68337521, -7.31662479}

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