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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