(2x^2)+16x+22=0

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Solution for (2x^2)+16x+22=0 equation: 


Simplifying
(2x2) + 16x + 22 = 0

Reorder the terms:
22 + 16x + (2x2) = 0

Solving
22 + 16x + (2x2) = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(11 + 8x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(11 + 8x + x2)' equal to zero and attempt to solve:

Simplifying
11 + 8x + x2 = 0

Solving
11 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + 8x + -11 + x2 = 0 + -11

Reorder the terms:
11 + -11 + 8x + x2 = 0 + -11

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

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

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 = -11 + 16

Reorder the terms:
16 + 8x + x2 = -11 + 16

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

Factor a perfect square on the left side:
(x + 4)(x + 4) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + 4) equal to 2.236067978 and -2.236067978.


Subproblem 1
x + 4 = 2.236067978

Simplifying
x + 4 = 2.236067978

Reorder the terms:
4 + x = 2.236067978

Solving
4 + x = 2.236067978

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 = 2.236067978 + -4

Combine like terms: 4 + -4 = 0
0 + x = 2.236067978 + -4
x = 2.236067978 + -4

Combine like terms: 2.236067978 + -4 = -1.763932022
x = -1.763932022

Simplifying
x = -1.763932022


Subproblem 2
x + 4 = -2.236067978

Simplifying
x + 4 = -2.236067978

Reorder the terms:
4 + x = -2.236067978

Solving
4 + x = -2.236067978

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 = -2.236067978 + -4

Combine like terms: 4 + -4 = 0
0 + x = -2.236067978 + -4
x = -2.236067978 + -4

Combine like terms: -2.236067978 + -4 = -6.236067978
x = -6.236067978

Simplifying
x = -6.236067978


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.763932022, -6.236067978}
Solution
x = {-1.763932022, -6.236067978}

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