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 = 140.25
110.25 + 21y + y2 = 140.25

Factor a perfect square on the left side:
(y + 10.5)(y + 10.5) = 140.25

Calculate the square root of the right side: 11.842719282

Break this problem into two subproblems by setting 
(y + 10.5) equal to 11.842719282 and -11.842719282.


Subproblem 1
y + 10.5 = 11.842719282

Simplifying
y + 10.5 = 11.842719282

Reorder the terms:
10.5 + y = 11.842719282

Solving
10.5 + y = 11.842719282

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 = 11.842719282 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + y = 11.842719282 + -10.5
y = 11.842719282 + -10.5

Combine like terms: 11.842719282 + -10.5 = 1.342719282
y = 1.342719282

Simplifying
y = 1.342719282


Subproblem 2
y + 10.5 = -11.842719282

Simplifying
y + 10.5 = -11.842719282

Reorder the terms:
10.5 + y = -11.842719282

Solving
10.5 + y = -11.842719282

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 = -11.842719282 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + y = -11.842719282 + -10.5
y = -11.842719282 + -10.5

Combine like terms: -11.842719282 + -10.5 = -22.342719282
y = -22.342719282

Simplifying
y = -22.342719282


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.342719282, -22.342719282}

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