y^2-16y+16=14

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Solution for y^2-16y+16=14 equation: 


Simplifying
y2 + -16y + 16 = 14

Reorder the terms:
16 + -16y + y2 = 14

Solving
16 + -16y + y2 = 14

Solving for variable 'y'.

Reorder the terms:
16 + -14 + -16y + y2 = 14 + -14

Combine like terms: 16 + -14 = 2
2 + -16y + y2 = 14 + -14

Combine like terms: 14 + -14 = 0
2 + -16y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -16y + -2 + y2 = 0 + -2

Reorder the terms:
2 + -2 + -16y + y2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -16y + y2 = 0 + -2
-16y + y2 = 0 + -2

Combine like terms: 0 + -2 = -2
-16y + y2 = -2

The y term is -16y.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16y + 64 + y2 = -2 + 64

Reorder the terms:
64 + -16y + y2 = -2 + 64

Combine like terms: -2 + 64 = 62
64 + -16y + y2 = 62

Factor a perfect square on the left side:
(y + -8)(y + -8) = 62

Calculate the square root of the right side: 7.874007874

Break this problem into two subproblems by setting 
(y + -8) equal to 7.874007874 and -7.874007874.


Subproblem 1
y + -8 = 7.874007874

Simplifying
y + -8 = 7.874007874

Reorder the terms:
-8 + y = 7.874007874

Solving
-8 + y = 7.874007874

Solving for variable 'y'.

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

Add '8' to each side of the equation.
-8 + 8 + y = 7.874007874 + 8

Combine like terms: -8 + 8 = 0
0 + y = 7.874007874 + 8
y = 7.874007874 + 8

Combine like terms: 7.874007874 + 8 = 15.874007874
y = 15.874007874

Simplifying
y = 15.874007874


Subproblem 2
y + -8 = -7.874007874

Simplifying
y + -8 = -7.874007874

Reorder the terms:
-8 + y = -7.874007874

Solving
-8 + y = -7.874007874

Solving for variable 'y'.

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

Add '8' to each side of the equation.
-8 + 8 + y = -7.874007874 + 8

Combine like terms: -8 + 8 = 0
0 + y = -7.874007874 + 8
y = -7.874007874 + 8

Combine like terms: -7.874007874 + 8 = 0.125992126
y = 0.125992126

Simplifying
y = 0.125992126


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {15.874007874, 0.125992126}

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