x^2+22x+24=0

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Solution for x^2+22x+24=0 equation: 


Simplifying
x2 + 22x + 24 = 0

Reorder the terms:
24 + 22x + x2 = 0

Solving
24 + 22x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + 22x + -24 + x2 = 0 + -24

Reorder the terms:
24 + -24 + 22x + x2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + 22x + x2 = 0 + -24
22x + x2 = 0 + -24

Combine like terms: 0 + -24 = -24
22x + x2 = -24

The x term is 22x.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22x + 121 + x2 = -24 + 121

Reorder the terms:
121 + 22x + x2 = -24 + 121

Combine like terms: -24 + 121 = 97
121 + 22x + x2 = 97

Factor a perfect square on the left side:
(x + 11)(x + 11) = 97

Calculate the square root of the right side: 9.848857802

Break this problem into two subproblems by setting 
(x + 11) equal to 9.848857802 and -9.848857802.


Subproblem 1
x + 11 = 9.848857802

Simplifying
x + 11 = 9.848857802

Reorder the terms:
11 + x = 9.848857802

Solving
11 + x = 9.848857802

Solving for variable 'x'.

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

Add '-11' to each side of the equation.
11 + -11 + x = 9.848857802 + -11

Combine like terms: 11 + -11 = 0
0 + x = 9.848857802 + -11
x = 9.848857802 + -11

Combine like terms: 9.848857802 + -11 = -1.151142198
x = -1.151142198

Simplifying
x = -1.151142198


Subproblem 2
x + 11 = -9.848857802

Simplifying
x + 11 = -9.848857802

Reorder the terms:
11 + x = -9.848857802

Solving
11 + x = -9.848857802

Solving for variable 'x'.

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

Add '-11' to each side of the equation.
11 + -11 + x = -9.848857802 + -11

Combine like terms: 11 + -11 = 0
0 + x = -9.848857802 + -11
x = -9.848857802 + -11

Combine like terms: -9.848857802 + -11 = -20.848857802
x = -20.848857802

Simplifying
x = -20.848857802


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.151142198, -20.848857802}

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