y^2+21y-2=0

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


Simplifying
y2 + 21y + -2 = 0

Reorder the terms:
-2 + 21y + y2 = 0

Solving
-2 + 21y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 21y + 2 + y2 = 0 + 2

Reorder the terms:
-2 + 2 + 21y + y2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 21y + y2 = 0 + 2
21y + y2 = 0 + 2

Combine like terms: 0 + 2 = 2
21y + y2 = 2

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 = 2 + 110.25

Reorder the terms:
110.25 + 21y + y2 = 2 + 110.25

Combine like terms: 2 + 110.25 = 112.25
110.25 + 21y + y2 = 112.25

Factor a perfect square on the left side:
(y + 10.5)(y + 10.5) = 112.25

Calculate the square root of the right side: 10.59481005

Break this problem into two subproblems by setting 
(y + 10.5) equal to 10.59481005 and -10.59481005.


Subproblem 1
y + 10.5 = 10.59481005

Simplifying
y + 10.5 = 10.59481005

Reorder the terms:
10.5 + y = 10.59481005

Solving
10.5 + y = 10.59481005

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 = 10.59481005 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + y = 10.59481005 + -10.5
y = 10.59481005 + -10.5

Combine like terms: 10.59481005 + -10.5 = 0.09481005
y = 0.09481005

Simplifying
y = 0.09481005


Subproblem 2
y + 10.5 = -10.59481005

Simplifying
y + 10.5 = -10.59481005

Reorder the terms:
10.5 + y = -10.59481005

Solving
10.5 + y = -10.59481005

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 = -10.59481005 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + y = -10.59481005 + -10.5
y = -10.59481005 + -10.5

Combine like terms: -10.59481005 + -10.5 = -21.09481005
y = -21.09481005

Simplifying
y = -21.09481005


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.09481005, -21.09481005}

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