y^2-16y+61=81

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Solution for y^2-16y+61=81 equation:


Simplifying
y2 + -16y + 61 = 81

Reorder the terms:
61 + -16y + y2 = 81

Solving
61 + -16y + y2 = 81

Solving for variable 'y'.

Reorder the terms:
61 + -81 + -16y + y2 = 81 + -81

Combine like terms: 61 + -81 = -20
-20 + -16y + y2 = 81 + -81

Combine like terms: 81 + -81 = 0
-20 + -16y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -16y + 20 + y2 = 0 + 20

Reorder the terms:
-20 + 20 + -16y + y2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -16y + y2 = 0 + 20
-16y + y2 = 0 + 20

Combine like terms: 0 + 20 = 20
-16y + y2 = 20

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 = 20 + 64

Reorder the terms:
64 + -16y + y2 = 20 + 64

Combine like terms: 20 + 64 = 84
64 + -16y + y2 = 84

Factor a perfect square on the left side:
(y + -8)(y + -8) = 84

Calculate the square root of the right side: 9.16515139

Break this problem into two subproblems by setting 
(y + -8) equal to 9.16515139 and -9.16515139.

Subproblem 1

y + -8 = 9.16515139 Simplifying y + -8 = 9.16515139 Reorder the terms: -8 + y = 9.16515139 Solving -8 + y = 9.16515139 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 = 9.16515139 + 8 Combine like terms: -8 + 8 = 0 0 + y = 9.16515139 + 8 y = 9.16515139 + 8 Combine like terms: 9.16515139 + 8 = 17.16515139 y = 17.16515139 Simplifying y = 17.16515139

Subproblem 2

y + -8 = -9.16515139 Simplifying y + -8 = -9.16515139 Reorder the terms: -8 + y = -9.16515139 Solving -8 + y = -9.16515139 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 = -9.16515139 + 8 Combine like terms: -8 + 8 = 0 0 + y = -9.16515139 + 8 y = -9.16515139 + 8 Combine like terms: -9.16515139 + 8 = -1.16515139 y = -1.16515139 Simplifying y = -1.16515139

Solution

The solution to the problem is based on the solutions from the subproblems. y = {17.16515139, -1.16515139}

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