y^2-3y-22=0

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


Simplifying
y2 + -3y + -22 = 0

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

Solving
-22 + -3y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + -3y + 22 + y2 = 0 + 22

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

Combine like terms: -22 + 22 = 0
0 + -3y + y2 = 0 + 22
-3y + y2 = 0 + 22

Combine like terms: 0 + 22 = 22
-3y + y2 = 22

The y term is -3y.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3y + 2.25 + y2 = 22 + 2.25

Reorder the terms:
2.25 + -3y + y2 = 22 + 2.25

Combine like terms: 22 + 2.25 = 24.25
2.25 + -3y + y2 = 24.25

Factor a perfect square on the left side:
(y + -1.5)(y + -1.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(y + -1.5) equal to 4.924428901 and -4.924428901.


Subproblem 1
y + -1.5 = 4.924428901

Simplifying
y + -1.5 = 4.924428901

Reorder the terms:
-1.5 + y = 4.924428901

Solving
-1.5 + y = 4.924428901

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = 4.924428901 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = 4.924428901 + 1.5
y = 4.924428901 + 1.5

Combine like terms: 4.924428901 + 1.5 = 6.424428901
y = 6.424428901

Simplifying
y = 6.424428901


Subproblem 2
y + -1.5 = -4.924428901

Simplifying
y + -1.5 = -4.924428901

Reorder the terms:
-1.5 + y = -4.924428901

Solving
-1.5 + y = -4.924428901

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = -4.924428901 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = -4.924428901 + 1.5
y = -4.924428901 + 1.5

Combine like terms: -4.924428901 + 1.5 = -3.424428901
y = -3.424428901

Simplifying
y = -3.424428901


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {6.424428901, -3.424428901}

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