2(x+5)(x+5)-22=0

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Solution for 2(x+5)(x+5)-22=0 equation: 


Simplifying
2(x + 5)(x + 5) + -22 = 0

Reorder the terms:
2(5 + x)(x + 5) + -22 = 0

Reorder the terms:
2(5 + x)(5 + x) + -22 = 0

Multiply (5 + x) * (5 + x)
2(5(5 + x) + x(5 + x)) + -22 = 0
2((5 * 5 + x * 5) + x(5 + x)) + -22 = 0
2((25 + 5x) + x(5 + x)) + -22 = 0
2(25 + 5x + (5 * x + x * x)) + -22 = 0
2(25 + 5x + (5x + x2)) + -22 = 0

Combine like terms: 5x + 5x = 10x
2(25 + 10x + x2) + -22 = 0
(25 * 2 + 10x * 2 + x2 * 2) + -22 = 0
(50 + 20x + 2x2) + -22 = 0

Reorder the terms:
50 + -22 + 20x + 2x2 = 0

Combine like terms: 50 + -22 = 28
28 + 20x + 2x2 = 0

Solving
28 + 20x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(14 + 10x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(14 + 10x + x2)' equal to zero and attempt to solve:

Simplifying
14 + 10x + x2 = 0

Solving
14 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + 10x + -14 + x2 = 0 + -14

Reorder the terms:
14 + -14 + 10x + x2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + 10x + x2 = 0 + -14
10x + x2 = 0 + -14

Combine like terms: 0 + -14 = -14
10x + x2 = -14

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = -14 + 25

Reorder the terms:
25 + 10x + x2 = -14 + 25

Combine like terms: -14 + 25 = 11
25 + 10x + x2 = 11

Factor a perfect square on the left side:
(x + 5)(x + 5) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + 5) equal to 3.31662479 and -3.31662479.


Subproblem 1
x + 5 = 3.31662479

Simplifying
x + 5 = 3.31662479

Reorder the terms:
5 + x = 3.31662479

Solving
5 + x = 3.31662479

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 3.31662479 + -5

Combine like terms: 5 + -5 = 0
0 + x = 3.31662479 + -5
x = 3.31662479 + -5

Combine like terms: 3.31662479 + -5 = -1.68337521
x = -1.68337521

Simplifying
x = -1.68337521


Subproblem 2
x + 5 = -3.31662479

Simplifying
x + 5 = -3.31662479

Reorder the terms:
5 + x = -3.31662479

Solving
5 + x = -3.31662479

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -3.31662479 + -5

Combine like terms: 5 + -5 = 0
0 + x = -3.31662479 + -5
x = -3.31662479 + -5

Combine like terms: -3.31662479 + -5 = -8.31662479
x = -8.31662479

Simplifying
x = -8.31662479


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.68337521, -8.31662479}
Solution
x = {-1.68337521, -8.31662479}

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