y^2-22y-19=0

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Solution for y^2-22y-19=0 equation: 


Simplifying
y2 + -22y + -19 = 0

Reorder the terms:
-19 + -22y + y2 = 0

Solving
-19 + -22y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + -22y + 19 + y2 = 0 + 19

Reorder the terms:
-19 + 19 + -22y + y2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -22y + y2 = 0 + 19
-22y + y2 = 0 + 19

Combine like terms: 0 + 19 = 19
-22y + y2 = 19

The y term is -22y.  Take half its coefficient (-11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
-22y + 121 + y2 = 19 + 121

Reorder the terms:
121 + -22y + y2 = 19 + 121

Combine like terms: 19 + 121 = 140
121 + -22y + y2 = 140

Factor a perfect square on the left side:
(y + -11)(y + -11) = 140

Calculate the square root of the right side: 11.832159566

Break this problem into two subproblems by setting 
(y + -11) equal to 11.832159566 and -11.832159566.


Subproblem 1
y + -11 = 11.832159566

Simplifying
y + -11 = 11.832159566

Reorder the terms:
-11 + y = 11.832159566

Solving
-11 + y = 11.832159566

Solving for variable 'y'.

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

Add '11' to each side of the equation.
-11 + 11 + y = 11.832159566 + 11

Combine like terms: -11 + 11 = 0
0 + y = 11.832159566 + 11
y = 11.832159566 + 11

Combine like terms: 11.832159566 + 11 = 22.832159566
y = 22.832159566

Simplifying
y = 22.832159566


Subproblem 2
y + -11 = -11.832159566

Simplifying
y + -11 = -11.832159566

Reorder the terms:
-11 + y = -11.832159566

Solving
-11 + y = -11.832159566

Solving for variable 'y'.

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

Add '11' to each side of the equation.
-11 + 11 + y = -11.832159566 + 11

Combine like terms: -11 + 11 = 0
0 + y = -11.832159566 + 11
y = -11.832159566 + 11

Combine like terms: -11.832159566 + 11 = -0.832159566
y = -0.832159566

Simplifying
y = -0.832159566


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {22.832159566, -0.832159566}

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