y^2+21y+30=0

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Solution for y^2+21y+30=0 equation: 


Simplifying
y2 + 21y + 30 = 0

Reorder the terms:
30 + 21y + y2 = 0

Solving
30 + 21y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-30' to each side of the equation.
30 + 21y + -30 + y2 = 0 + -30

Reorder the terms:
30 + -30 + 21y + y2 = 0 + -30

Combine like terms: 30 + -30 = 0
0 + 21y + y2 = 0 + -30
21y + y2 = 0 + -30

Combine like terms: 0 + -30 = -30
21y + y2 = -30

The y term is 21y.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21y + 110.25 + y2 = -30 + 110.25

Reorder the terms:
110.25 + 21y + y2 = -30 + 110.25

Combine like terms: -30 + 110.25 = 80.25
110.25 + 21y + y2 = 80.25

Factor a perfect square on the left side:
(y + 10.5)(y + 10.5) = 80.25

Calculate the square root of the right side: 8.958236434

Break this problem into two subproblems by setting 
(y + 10.5) equal to 8.958236434 and -8.958236434.


Subproblem 1
y + 10.5 = 8.958236434

Simplifying
y + 10.5 = 8.958236434

Reorder the terms:
10.5 + y = 8.958236434

Solving
10.5 + y = 8.958236434

Solving for variable 'y'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + y = 8.958236434 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + y = 8.958236434 + -10.5
y = 8.958236434 + -10.5

Combine like terms: 8.958236434 + -10.5 = -1.541763566
y = -1.541763566

Simplifying
y = -1.541763566


Subproblem 2
y + 10.5 = -8.958236434

Simplifying
y + 10.5 = -8.958236434

Reorder the terms:
10.5 + y = -8.958236434

Solving
10.5 + y = -8.958236434

Solving for variable 'y'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + y = -8.958236434 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + y = -8.958236434 + -10.5
y = -8.958236434 + -10.5

Combine like terms: -8.958236434 + -10.5 = -19.458236434
y = -19.458236434

Simplifying
y = -19.458236434


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-1.541763566, -19.458236434}

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