y^2-8y+16=24

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Solution for y^2-8y+16=24 equation: 


Simplifying
y2 + -8y + 16 = 24

Reorder the terms:
16 + -8y + y2 = 24

Solving
16 + -8y + y2 = 24

Solving for variable 'y'.

Reorder the terms:
16 + -24 + -8y + y2 = 24 + -24

Combine like terms: 16 + -24 = -8
-8 + -8y + y2 = 24 + -24

Combine like terms: 24 + -24 = 0
-8 + -8y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -8y + 8 + y2 = 0 + 8

Reorder the terms:
-8 + 8 + -8y + y2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -8y + y2 = 0 + 8
-8y + y2 = 0 + 8

Combine like terms: 0 + 8 = 8
-8y + y2 = 8

The y term is -8y.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8y + 16 + y2 = 8 + 16

Reorder the terms:
16 + -8y + y2 = 8 + 16

Combine like terms: 8 + 16 = 24
16 + -8y + y2 = 24

Factor a perfect square on the left side:
(y + -4)(y + -4) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(y + -4) equal to 4.898979486 and -4.898979486.


Subproblem 1
y + -4 = 4.898979486

Simplifying
y + -4 = 4.898979486

Reorder the terms:
-4 + y = 4.898979486

Solving
-4 + y = 4.898979486

Solving for variable 'y'.

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

Add '4' to each side of the equation.
-4 + 4 + y = 4.898979486 + 4

Combine like terms: -4 + 4 = 0
0 + y = 4.898979486 + 4
y = 4.898979486 + 4

Combine like terms: 4.898979486 + 4 = 8.898979486
y = 8.898979486

Simplifying
y = 8.898979486


Subproblem 2
y + -4 = -4.898979486

Simplifying
y + -4 = -4.898979486

Reorder the terms:
-4 + y = -4.898979486

Solving
-4 + y = -4.898979486

Solving for variable 'y'.

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

Add '4' to each side of the equation.
-4 + 4 + y = -4.898979486 + 4

Combine like terms: -4 + 4 = 0
0 + y = -4.898979486 + 4
y = -4.898979486 + 4

Combine like terms: -4.898979486 + 4 = -0.898979486
y = -0.898979486

Simplifying
y = -0.898979486


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {8.898979486, -0.898979486}

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