y^2+22y-24=0

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Solution for y^2+22y-24=0 equation: 


Simplifying
y2 + 22y + -24 = 0

Reorder the terms:
-24 + 22y + y2 = 0

Solving
-24 + 22y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + 22y + 24 + y2 = 0 + 24

Reorder the terms:
-24 + 24 + 22y + y2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 22y + y2 = 0 + 24
22y + y2 = 0 + 24

Combine like terms: 0 + 24 = 24
22y + y2 = 24

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

Add '121' to each side of the equation.
22y + 121 + y2 = 24 + 121

Reorder the terms:
121 + 22y + y2 = 24 + 121

Combine like terms: 24 + 121 = 145
121 + 22y + y2 = 145

Factor a perfect square on the left side:
(y + 11)(y + 11) = 145

Calculate the square root of the right side: 12.041594579

Break this problem into two subproblems by setting 
(y + 11) equal to 12.041594579 and -12.041594579.


Subproblem 1
y + 11 = 12.041594579

Simplifying
y + 11 = 12.041594579

Reorder the terms:
11 + y = 12.041594579

Solving
11 + y = 12.041594579

Solving for variable 'y'.

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

Add '-11' to each side of the equation.
11 + -11 + y = 12.041594579 + -11

Combine like terms: 11 + -11 = 0
0 + y = 12.041594579 + -11
y = 12.041594579 + -11

Combine like terms: 12.041594579 + -11 = 1.041594579
y = 1.041594579

Simplifying
y = 1.041594579


Subproblem 2
y + 11 = -12.041594579

Simplifying
y + 11 = -12.041594579

Reorder the terms:
11 + y = -12.041594579

Solving
11 + y = -12.041594579

Solving for variable 'y'.

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

Add '-11' to each side of the equation.
11 + -11 + y = -12.041594579 + -11

Combine like terms: 11 + -11 = 0
0 + y = -12.041594579 + -11
y = -12.041594579 + -11

Combine like terms: -12.041594579 + -11 = -23.041594579
y = -23.041594579

Simplifying
y = -23.041594579


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.041594579, -23.041594579}

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