32y-y^2=2

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Solution for 32y-y^2=2 equation: 


Simplifying
32y + -1y2 = 2

Solving
32y + -1y2 = 2

Solving for variable 'y'.

Reorder the terms:
-2 + 32y + -1y2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 32y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
2 + -32y + y2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -32y + -2 + y2 = 0 + -2

Reorder the terms:
2 + -2 + -32y + y2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -32y + y2 = 0 + -2
-32y + y2 = 0 + -2

Combine like terms: 0 + -2 = -2
-32y + y2 = -2

The y term is -32y.  Take half its coefficient (-16).
Square it (256) and add it to both sides.

Add '256' to each side of the equation.
-32y + 256 + y2 = -2 + 256

Reorder the terms:
256 + -32y + y2 = -2 + 256

Combine like terms: -2 + 256 = 254
256 + -32y + y2 = 254

Factor a perfect square on the left side:
(y + -16)(y + -16) = 254

Calculate the square root of the right side: 15.937377451

Break this problem into two subproblems by setting 
(y + -16) equal to 15.937377451 and -15.937377451.


Subproblem 1
y + -16 = 15.937377451

Simplifying
y + -16 = 15.937377451

Reorder the terms:
-16 + y = 15.937377451

Solving
-16 + y = 15.937377451

Solving for variable 'y'.

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

Add '16' to each side of the equation.
-16 + 16 + y = 15.937377451 + 16

Combine like terms: -16 + 16 = 0
0 + y = 15.937377451 + 16
y = 15.937377451 + 16

Combine like terms: 15.937377451 + 16 = 31.937377451
y = 31.937377451

Simplifying
y = 31.937377451


Subproblem 2
y + -16 = -15.937377451

Simplifying
y + -16 = -15.937377451

Reorder the terms:
-16 + y = -15.937377451

Solving
-16 + y = -15.937377451

Solving for variable 'y'.

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

Add '16' to each side of the equation.
-16 + 16 + y = -15.937377451 + 16

Combine like terms: -16 + 16 = 0
0 + y = -15.937377451 + 16
y = -15.937377451 + 16

Combine like terms: -15.937377451 + 16 = 0.062622549
y = 0.062622549

Simplifying
y = 0.062622549


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {31.937377451, 0.062622549}

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