y(y-10)=16

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Solution for y(y-10)=16 equation: 


Simplifying
y(y + -10) = 16

Reorder the terms:
y(-10 + y) = 16
(-10 * y + y * y) = 16
(-10y + y2) = 16

Solving
-10y + y2 = 16

Solving for variable 'y'.

Reorder the terms:
-16 + -10y + y2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + -10y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -10y + 16 + y2 = 0 + 16

Reorder the terms:
-16 + 16 + -10y + y2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -10y + y2 = 0 + 16
-10y + y2 = 0 + 16

Combine like terms: 0 + 16 = 16
-10y + y2 = 16

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 = 16 + 25

Reorder the terms:
25 + -10y + y2 = 16 + 25

Combine like terms: 16 + 25 = 41
25 + -10y + y2 = 41

Factor a perfect square on the left side:
(y + -5)(y + -5) = 41

Calculate the square root of the right side: 6.403124237

Break this problem into two subproblems by setting 
(y + -5) equal to 6.403124237 and -6.403124237.


Subproblem 1
y + -5 = 6.403124237

Simplifying
y + -5 = 6.403124237

Reorder the terms:
-5 + y = 6.403124237

Solving
-5 + y = 6.403124237

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 = 6.403124237 + 5

Combine like terms: -5 + 5 = 0
0 + y = 6.403124237 + 5
y = 6.403124237 + 5

Combine like terms: 6.403124237 + 5 = 11.403124237
y = 11.403124237

Simplifying
y = 11.403124237


Subproblem 2
y + -5 = -6.403124237

Simplifying
y + -5 = -6.403124237

Reorder the terms:
-5 + y = -6.403124237

Solving
-5 + y = -6.403124237

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 = -6.403124237 + 5

Combine like terms: -5 + 5 = 0
0 + y = -6.403124237 + 5
y = -6.403124237 + 5

Combine like terms: -6.403124237 + 5 = -1.403124237
y = -1.403124237

Simplifying
y = -1.403124237


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {11.403124237, -1.403124237}

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