y^2-10y=-20

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Solution for y^2-10y=-20 equation: 


Simplifying
y2 + -10y = -20

Reorder the terms:
-10y + y2 = -20

Solving
-10y + y2 = -20

Solving for variable 'y'.

Reorder the terms:
20 + -10y + y2 = -20 + 20

Combine like terms: -20 + 20 = 0
20 + -10y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + -10y + -20 + y2 = 0 + -20

Reorder the terms:
20 + -20 + -10y + y2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -10y + y2 = 0 + -20
-10y + y2 = 0 + -20

Combine like terms: 0 + -20 = -20
-10y + y2 = -20

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 = -20 + 25

Reorder the terms:
25 + -10y + y2 = -20 + 25

Combine like terms: -20 + 25 = 5
25 + -10y + y2 = 5

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

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(y + -5) equal to 2.236067978 and -2.236067978.


Subproblem 1
y + -5 = 2.236067978

Simplifying
y + -5 = 2.236067978

Reorder the terms:
-5 + y = 2.236067978

Solving
-5 + y = 2.236067978

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 = 2.236067978 + 5

Combine like terms: -5 + 5 = 0
0 + y = 2.236067978 + 5
y = 2.236067978 + 5

Combine like terms: 2.236067978 + 5 = 7.236067978
y = 7.236067978

Simplifying
y = 7.236067978


Subproblem 2
y + -5 = -2.236067978

Simplifying
y + -5 = -2.236067978

Reorder the terms:
-5 + y = -2.236067978

Solving
-5 + y = -2.236067978

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 = -2.236067978 + 5

Combine like terms: -5 + 5 = 0
0 + y = -2.236067978 + 5
y = -2.236067978 + 5

Combine like terms: -2.236067978 + 5 = 2.763932022
y = 2.763932022

Simplifying
y = 2.763932022


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {7.236067978, 2.763932022}

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