y^2-8y-22=0

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Solution for y^2-8y-22=0 equation: 


Simplifying
y2 + -8y + -22 = 0

Reorder the terms:
-22 + -8y + y2 = 0

Solving
-22 + -8y + 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 + -8y + 22 + y2 = 0 + 22

Reorder the terms:
-22 + 22 + -8y + y2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -8y + y2 = 0 + 22
-8y + y2 = 0 + 22

Combine like terms: 0 + 22 = 22
-8y + y2 = 22

The y term is -8y.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8y + 16 + y2 = 22 + 16

Reorder the terms:
16 + -8y + y2 = 22 + 16

Combine like terms: 22 + 16 = 38
16 + -8y + y2 = 38

Factor a perfect square on the left side:
(y + -4)(y + -4) = 38

Calculate the square root of the right side: 6.164414003

Break this problem into two subproblems by setting 
(y + -4) equal to 6.164414003 and -6.164414003.


Subproblem 1
y + -4 = 6.164414003

Simplifying
y + -4 = 6.164414003

Reorder the terms:
-4 + y = 6.164414003

Solving
-4 + y = 6.164414003

Solving for variable 'y'.

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

Add '4' to each side of the equation.
-4 + 4 + y = 6.164414003 + 4

Combine like terms: -4 + 4 = 0
0 + y = 6.164414003 + 4
y = 6.164414003 + 4

Combine like terms: 6.164414003 + 4 = 10.164414003
y = 10.164414003

Simplifying
y = 10.164414003


Subproblem 2
y + -4 = -6.164414003

Simplifying
y + -4 = -6.164414003

Reorder the terms:
-4 + y = -6.164414003

Solving
-4 + y = -6.164414003

Solving for variable 'y'.

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

Add '4' to each side of the equation.
-4 + 4 + y = -6.164414003 + 4

Combine like terms: -4 + 4 = 0
0 + y = -6.164414003 + 4
y = -6.164414003 + 4

Combine like terms: -6.164414003 + 4 = -2.164414003
y = -2.164414003

Simplifying
y = -2.164414003


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {10.164414003, -2.164414003}

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