y^2-16y+62=0

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Solution for y^2-16y+62=0 equation: 


Simplifying
y2 + -16y + 62 = 0

Reorder the terms:
62 + -16y + y2 = 0

Solving
62 + -16y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-62' to each side of the equation.
62 + -16y + -62 + y2 = 0 + -62

Reorder the terms:
62 + -62 + -16y + y2 = 0 + -62

Combine like terms: 62 + -62 = 0
0 + -16y + y2 = 0 + -62
-16y + y2 = 0 + -62

Combine like terms: 0 + -62 = -62
-16y + y2 = -62

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 = -62 + 64

Reorder the terms:
64 + -16y + y2 = -62 + 64

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

Factor a perfect square on the left side:
(y + -8)(y + -8) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(y + -8) equal to 1.414213562 and -1.414213562.


Subproblem 1
y + -8 = 1.414213562

Simplifying
y + -8 = 1.414213562

Reorder the terms:
-8 + y = 1.414213562

Solving
-8 + y = 1.414213562

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 = 1.414213562 + 8

Combine like terms: -8 + 8 = 0
0 + y = 1.414213562 + 8
y = 1.414213562 + 8

Combine like terms: 1.414213562 + 8 = 9.414213562
y = 9.414213562

Simplifying
y = 9.414213562


Subproblem 2
y + -8 = -1.414213562

Simplifying
y + -8 = -1.414213562

Reorder the terms:
-8 + y = -1.414213562

Solving
-8 + y = -1.414213562

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 = -1.414213562 + 8

Combine like terms: -8 + 8 = 0
0 + y = -1.414213562 + 8
y = -1.414213562 + 8

Combine like terms: -1.414213562 + 8 = 6.585786438
y = 6.585786438

Simplifying
y = 6.585786438


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {9.414213562, 6.585786438}

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