y^2-12y+16=0

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Solution for y^2-12y+16=0 equation: 


Simplifying
y2 + -12y + 16 = 0

Reorder the terms:
16 + -12y + y2 = 0

Solving
16 + -12y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -12y + -16 + y2 = 0 + -16

Reorder the terms:
16 + -16 + -12y + y2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -12y + y2 = 0 + -16
-12y + y2 = 0 + -16

Combine like terms: 0 + -16 = -16
-12y + y2 = -16

The y term is -12y.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12y + 36 + y2 = -16 + 36

Reorder the terms:
36 + -12y + y2 = -16 + 36

Combine like terms: -16 + 36 = 20
36 + -12y + y2 = 20

Factor a perfect square on the left side:
(y + -6)(y + -6) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(y + -6) equal to 4.472135955 and -4.472135955.


Subproblem 1
y + -6 = 4.472135955

Simplifying
y + -6 = 4.472135955

Reorder the terms:
-6 + y = 4.472135955

Solving
-6 + y = 4.472135955

Solving for variable 'y'.

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

Add '6' to each side of the equation.
-6 + 6 + y = 4.472135955 + 6

Combine like terms: -6 + 6 = 0
0 + y = 4.472135955 + 6
y = 4.472135955 + 6

Combine like terms: 4.472135955 + 6 = 10.472135955
y = 10.472135955

Simplifying
y = 10.472135955


Subproblem 2
y + -6 = -4.472135955

Simplifying
y + -6 = -4.472135955

Reorder the terms:
-6 + y = -4.472135955

Solving
-6 + y = -4.472135955

Solving for variable 'y'.

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

Add '6' to each side of the equation.
-6 + 6 + y = -4.472135955 + 6

Combine like terms: -6 + 6 = 0
0 + y = -4.472135955 + 6
y = -4.472135955 + 6

Combine like terms: -4.472135955 + 6 = 1.527864045
y = 1.527864045

Simplifying
y = 1.527864045


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {10.472135955, 1.527864045}

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