y^2-16=2y

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


Simplifying
y2 + -16 = 2y

Reorder the terms:
-16 + y2 = 2y

Solving
-16 + y2 = 2y

Solving for variable 'y'.

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

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

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The y term is -2y.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2y + 1 + y2 = 16 + 1

Reorder the terms:
1 + -2y + y2 = 16 + 1

Combine like terms: 16 + 1 = 17
1 + -2y + y2 = 17

Factor a perfect square on the left side:
(y + -1)(y + -1) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(y + -1) equal to 4.123105626 and -4.123105626.

Subproblem 1

y + -1 = 4.123105626 Simplifying y + -1 = 4.123105626 Reorder the terms: -1 + y = 4.123105626 Solving -1 + y = 4.123105626 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = 4.123105626 + 1 Combine like terms: -1 + 1 = 0 0 + y = 4.123105626 + 1 y = 4.123105626 + 1 Combine like terms: 4.123105626 + 1 = 5.123105626 y = 5.123105626 Simplifying y = 5.123105626

Subproblem 2

y + -1 = -4.123105626 Simplifying y + -1 = -4.123105626 Reorder the terms: -1 + y = -4.123105626 Solving -1 + y = -4.123105626 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = -4.123105626 + 1 Combine like terms: -1 + 1 = 0 0 + y = -4.123105626 + 1 y = -4.123105626 + 1 Combine like terms: -4.123105626 + 1 = -3.123105626 y = -3.123105626 Simplifying y = -3.123105626

Solution

The solution to the problem is based on the solutions from the subproblems. y = {5.123105626, -3.123105626}

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