2x^2+22x+30=0

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Solution for 2x^2+22x+30=0 equation: 


Simplifying
2x2 + 22x + 30 = 0

Reorder the terms:
30 + 22x + 2x2 = 0

Solving
30 + 22x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + 11x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(15 + 11x + x2)' equal to zero and attempt to solve:

Simplifying
15 + 11x + x2 = 0

Solving
15 + 11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + 11x + -15 + x2 = 0 + -15

Reorder the terms:
15 + -15 + 11x + x2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 11x + x2 = 0 + -15
11x + x2 = 0 + -15

Combine like terms: 0 + -15 = -15
11x + x2 = -15

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = -15 + 30.25

Reorder the terms:
30.25 + 11x + x2 = -15 + 30.25

Combine like terms: -15 + 30.25 = 15.25
30.25 + 11x + x2 = 15.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(x + 5.5) equal to 3.905124838 and -3.905124838.


Subproblem 1
x + 5.5 = 3.905124838

Simplifying
x + 5.5 = 3.905124838

Reorder the terms:
5.5 + x = 3.905124838

Solving
5.5 + x = 3.905124838

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = 3.905124838 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 3.905124838 + -5.5
x = 3.905124838 + -5.5

Combine like terms: 3.905124838 + -5.5 = -1.594875162
x = -1.594875162

Simplifying
x = -1.594875162


Subproblem 2
x + 5.5 = -3.905124838

Simplifying
x + 5.5 = -3.905124838

Reorder the terms:
5.5 + x = -3.905124838

Solving
5.5 + x = -3.905124838

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = -3.905124838 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -3.905124838 + -5.5
x = -3.905124838 + -5.5

Combine like terms: -3.905124838 + -5.5 = -9.405124838
x = -9.405124838

Simplifying
x = -9.405124838


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.594875162, -9.405124838}
Solution
x = {-1.594875162, -9.405124838}

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