3y^2-3y-22=0

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Solution for 3y^2-3y-22=0 equation: 


Simplifying
3y2 + -3y + -22 = 0

Reorder the terms:
-22 + -3y + 3y2 = 0

Solving
-22 + -3y + 3y2 = 0

Solving for variable 'y'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-7.333333333 + -1y + y2 = 0

Move the constant term to the right:

Add '7.333333333' to each side of the equation.
-7.333333333 + -1y + 7.333333333 + y2 = 0 + 7.333333333

Reorder the terms:
-7.333333333 + 7.333333333 + -1y + y2 = 0 + 7.333333333

Combine like terms: -7.333333333 + 7.333333333 = 0.000000000
0.000000000 + -1y + y2 = 0 + 7.333333333
-1y + y2 = 0 + 7.333333333

Combine like terms: 0 + 7.333333333 = 7.333333333
-1y + y2 = 7.333333333

The y term is -1y.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1y + 0.25 + y2 = 7.333333333 + 0.25

Reorder the terms:
0.25 + -1y + y2 = 7.333333333 + 0.25

Combine like terms: 7.333333333 + 0.25 = 7.583333333
0.25 + -1y + y2 = 7.583333333

Factor a perfect square on the left side:
(y + -0.5)(y + -0.5) = 7.583333333

Calculate the square root of the right side: 2.753785274

Break this problem into two subproblems by setting 
(y + -0.5) equal to 2.753785274 and -2.753785274.


Subproblem 1
y + -0.5 = 2.753785274

Simplifying
y + -0.5 = 2.753785274

Reorder the terms:
-0.5 + y = 2.753785274

Solving
-0.5 + y = 2.753785274

Solving for variable 'y'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + y = 2.753785274 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y = 2.753785274 + 0.5
y = 2.753785274 + 0.5

Combine like terms: 2.753785274 + 0.5 = 3.253785274
y = 3.253785274

Simplifying
y = 3.253785274


Subproblem 2
y + -0.5 = -2.753785274

Simplifying
y + -0.5 = -2.753785274

Reorder the terms:
-0.5 + y = -2.753785274

Solving
-0.5 + y = -2.753785274

Solving for variable 'y'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + y = -2.753785274 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y = -2.753785274 + 0.5
y = -2.753785274 + 0.5

Combine like terms: -2.753785274 + 0.5 = -2.253785274
y = -2.253785274

Simplifying
y = -2.253785274


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.253785274, -2.253785274}

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