y^2=8y+16

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


Simplifying
y2 = 8y + 16

Reorder the terms:
y2 = 16 + 8y

Solving
y2 = 16 + 8y

Solving for variable 'y'.

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

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

Combine like terms: 16 + -16 = 0
-16 + -8y + y2 = 0 + 8y + -8y
-16 + -8y + y2 = 8y + -8y

Combine like terms: 8y + -8y = 0
-16 + -8y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -8y + 16 + y2 = 0 + 16

Reorder the terms:
-16 + 16 + -8y + y2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -8y + y2 = 0 + 16
-8y + y2 = 0 + 16

Combine like terms: 0 + 16 = 16
-8y + y2 = 16

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 = 16 + 16

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

Combine like terms: 16 + 16 = 32
16 + -8y + y2 = 32

Factor a perfect square on the left side:
(y + -4)(y + -4) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(y + -4) equal to 5.656854249 and -5.656854249.

Subproblem 1

y + -4 = 5.656854249 Simplifying y + -4 = 5.656854249 Reorder the terms: -4 + y = 5.656854249 Solving -4 + y = 5.656854249 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 = 5.656854249 + 4 Combine like terms: -4 + 4 = 0 0 + y = 5.656854249 + 4 y = 5.656854249 + 4 Combine like terms: 5.656854249 + 4 = 9.656854249 y = 9.656854249 Simplifying y = 9.656854249

Subproblem 2

y + -4 = -5.656854249 Simplifying y + -4 = -5.656854249 Reorder the terms: -4 + y = -5.656854249 Solving -4 + y = -5.656854249 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 = -5.656854249 + 4 Combine like terms: -4 + 4 = 0 0 + y = -5.656854249 + 4 y = -5.656854249 + 4 Combine like terms: -5.656854249 + 4 = -1.656854249 y = -1.656854249 Simplifying y = -1.656854249

Solution

The solution to the problem is based on the solutions from the subproblems. y = {9.656854249, -1.656854249}

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