5y=16-y^2

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Solution for 5y=16-y^2 equation:


Simplifying
5y = 16 + -1y2

Solving
5y = 16 + -1y2

Solving for variable 'y'.

Reorder the terms:
-16 + 5y + y2 = 16 + -1y2 + -16 + y2

Reorder the terms:
-16 + 5y + y2 = 16 + -16 + -1y2 + y2

Combine like terms: 16 + -16 = 0
-16 + 5y + y2 = 0 + -1y2 + y2
-16 + 5y + y2 = -1y2 + y2

Combine like terms: -1y2 + y2 = 0
-16 + 5y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 5y + 16 + y2 = 0 + 16

Reorder the terms:
-16 + 16 + 5y + y2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 5y + y2 = 0 + 16
5y + y2 = 0 + 16

Combine like terms: 0 + 16 = 16
5y + y2 = 16

The y term is 5y.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5y + 6.25 + y2 = 16 + 6.25

Reorder the terms:
6.25 + 5y + y2 = 16 + 6.25

Combine like terms: 16 + 6.25 = 22.25
6.25 + 5y + y2 = 22.25

Factor a perfect square on the left side:
(y + 2.5)(y + 2.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(y + 2.5) equal to 4.716990566 and -4.716990566.

Subproblem 1

y + 2.5 = 4.716990566 Simplifying y + 2.5 = 4.716990566 Reorder the terms: 2.5 + y = 4.716990566 Solving 2.5 + y = 4.716990566 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + y = 4.716990566 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + y = 4.716990566 + -2.5 y = 4.716990566 + -2.5 Combine like terms: 4.716990566 + -2.5 = 2.216990566 y = 2.216990566 Simplifying y = 2.216990566

Subproblem 2

y + 2.5 = -4.716990566 Simplifying y + 2.5 = -4.716990566 Reorder the terms: 2.5 + y = -4.716990566 Solving 2.5 + y = -4.716990566 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + y = -4.716990566 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + y = -4.716990566 + -2.5 y = -4.716990566 + -2.5 Combine like terms: -4.716990566 + -2.5 = -7.216990566 y = -7.216990566 Simplifying y = -7.216990566

Solution

The solution to the problem is based on the solutions from the subproblems. y = {2.216990566, -7.216990566}

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