y^2+20y+24=0

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Solution for y^2+20y+24=0 equation: 


Simplifying
y2 + 20y + 24 = 0

Reorder the terms:
24 + 20y + y2 = 0

Solving
24 + 20y + 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 + 20y + -24 + y2 = 0 + -24

Reorder the terms:
24 + -24 + 20y + y2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + 20y + y2 = 0 + -24
20y + y2 = 0 + -24

Combine like terms: 0 + -24 = -24
20y + y2 = -24

The y term is 20y.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20y + 100 + y2 = -24 + 100

Reorder the terms:
100 + 20y + y2 = -24 + 100

Combine like terms: -24 + 100 = 76
100 + 20y + y2 = 76

Factor a perfect square on the left side:
(y + 10)(y + 10) = 76

Calculate the square root of the right side: 8.717797887

Break this problem into two subproblems by setting 
(y + 10) equal to 8.717797887 and -8.717797887.


Subproblem 1
y + 10 = 8.717797887

Simplifying
y + 10 = 8.717797887

Reorder the terms:
10 + y = 8.717797887

Solving
10 + y = 8.717797887

Solving for variable 'y'.

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

Add '-10' to each side of the equation.
10 + -10 + y = 8.717797887 + -10

Combine like terms: 10 + -10 = 0
0 + y = 8.717797887 + -10
y = 8.717797887 + -10

Combine like terms: 8.717797887 + -10 = -1.282202113
y = -1.282202113

Simplifying
y = -1.282202113


Subproblem 2
y + 10 = -8.717797887

Simplifying
y + 10 = -8.717797887

Reorder the terms:
10 + y = -8.717797887

Solving
10 + y = -8.717797887

Solving for variable 'y'.

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

Add '-10' to each side of the equation.
10 + -10 + y = -8.717797887 + -10

Combine like terms: 10 + -10 = 0
0 + y = -8.717797887 + -10
y = -8.717797887 + -10

Combine like terms: -8.717797887 + -10 = -18.717797887
y = -18.717797887

Simplifying
y = -18.717797887


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-1.282202113, -18.717797887}

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