y^2-16y+64=7

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Solution for y^2-16y+64=7 equation: 


Simplifying
y2 + -16y + 64 = 7

Reorder the terms:
64 + -16y + y2 = 7

Solving
64 + -16y + y2 = 7

Solving for variable 'y'.

Reorder the terms:
64 + -7 + -16y + y2 = 7 + -7

Combine like terms: 64 + -7 = 57
57 + -16y + y2 = 7 + -7

Combine like terms: 7 + -7 = 0
57 + -16y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-57' to each side of the equation.
57 + -16y + -57 + y2 = 0 + -57

Reorder the terms:
57 + -57 + -16y + y2 = 0 + -57

Combine like terms: 57 + -57 = 0
0 + -16y + y2 = 0 + -57
-16y + y2 = 0 + -57

Combine like terms: 0 + -57 = -57
-16y + y2 = -57

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 = -57 + 64

Reorder the terms:
64 + -16y + y2 = -57 + 64

Combine like terms: -57 + 64 = 7
64 + -16y + y2 = 7

Factor a perfect square on the left side:
(y + -8)(y + -8) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(y + -8) equal to 2.645751311 and -2.645751311.


Subproblem 1
y + -8 = 2.645751311

Simplifying
y + -8 = 2.645751311

Reorder the terms:
-8 + y = 2.645751311

Solving
-8 + y = 2.645751311

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 = 2.645751311 + 8

Combine like terms: -8 + 8 = 0
0 + y = 2.645751311 + 8
y = 2.645751311 + 8

Combine like terms: 2.645751311 + 8 = 10.645751311
y = 10.645751311

Simplifying
y = 10.645751311


Subproblem 2
y + -8 = -2.645751311

Simplifying
y + -8 = -2.645751311

Reorder the terms:
-8 + y = -2.645751311

Solving
-8 + y = -2.645751311

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 = -2.645751311 + 8

Combine like terms: -8 + 8 = 0
0 + y = -2.645751311 + 8
y = -2.645751311 + 8

Combine like terms: -2.645751311 + 8 = 5.354248689
y = 5.354248689

Simplifying
y = 5.354248689


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {10.645751311, 5.354248689}

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