y^2-10y-22=0

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Solution for y^2-10y-22=0 equation: 


Simplifying
y2 + -10y + -22 = 0

Reorder the terms:
-22 + -10y + y2 = 0

Solving
-22 + -10y + 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 + -10y + 22 + y2 = 0 + 22

Reorder the terms:
-22 + 22 + -10y + y2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -10y + y2 = 0 + 22
-10y + y2 = 0 + 22

Combine like terms: 0 + 22 = 22
-10y + y2 = 22

The y term is -10y.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10y + 25 + y2 = 22 + 25

Reorder the terms:
25 + -10y + y2 = 22 + 25

Combine like terms: 22 + 25 = 47
25 + -10y + y2 = 47

Factor a perfect square on the left side:
(y + -5)(y + -5) = 47

Calculate the square root of the right side: 6.8556546

Break this problem into two subproblems by setting 
(y + -5) equal to 6.8556546 and -6.8556546.


Subproblem 1
y + -5 = 6.8556546

Simplifying
y + -5 = 6.8556546

Reorder the terms:
-5 + y = 6.8556546

Solving
-5 + y = 6.8556546

Solving for variable 'y'.

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

Add '5' to each side of the equation.
-5 + 5 + y = 6.8556546 + 5

Combine like terms: -5 + 5 = 0
0 + y = 6.8556546 + 5
y = 6.8556546 + 5

Combine like terms: 6.8556546 + 5 = 11.8556546
y = 11.8556546

Simplifying
y = 11.8556546


Subproblem 2
y + -5 = -6.8556546

Simplifying
y + -5 = -6.8556546

Reorder the terms:
-5 + y = -6.8556546

Solving
-5 + y = -6.8556546

Solving for variable 'y'.

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

Add '5' to each side of the equation.
-5 + 5 + y = -6.8556546 + 5

Combine like terms: -5 + 5 = 0
0 + y = -6.8556546 + 5
y = -6.8556546 + 5

Combine like terms: -6.8556546 + 5 = -1.8556546
y = -1.8556546

Simplifying
y = -1.8556546


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {11.8556546, -1.8556546}

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