y^2-5y=28.5

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Solution for y^2-5y=28.5 equation:


Simplifying
y2 + -5y = 28.5

Reorder the terms:
-5y + y2 = 28.5

Solving
-5y + y2 = 28.5

Solving for variable 'y'.

Reorder the terms:
-28.5 + -5y + y2 = 28.5 + -28.5

Combine like terms: 28.5 + -28.5 = 0.0
-28.5 + -5y + y2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '28.5' to each side of the equation.
-28.5 + -5y + 28.5 + y2 = 0.0 + 28.5

Reorder the terms:
-28.5 + 28.5 + -5y + y2 = 0.0 + 28.5

Combine like terms: -28.5 + 28.5 = 0.0
0.0 + -5y + y2 = 0.0 + 28.5
-5y + y2 = 0.0 + 28.5

Combine like terms: 0.0 + 28.5 = 28.5
-5y + y2 = 28.5

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 = 28.5 + 6.25

Reorder the terms:
6.25 + -5y + y2 = 28.5 + 6.25

Combine like terms: 28.5 + 6.25 = 34.75
6.25 + -5y + y2 = 34.75

Factor a perfect square on the left side:
(y + -2.5)(y + -2.5) = 34.75

Calculate the square root of the right side: 5.894913061

Break this problem into two subproblems by setting 
(y + -2.5) equal to 5.894913061 and -5.894913061.


Subproblem 1
y + -2.5 = 5.894913061

Simplifying
y + -2.5 = 5.894913061

Reorder the terms:
-2.5 + y = 5.894913061

Solving
-2.5 + y = 5.894913061

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 = 5.894913061 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + y = 5.894913061 + 2.5
y = 5.894913061 + 2.5

Combine like terms: 5.894913061 + 2.5 = 8.394913061
y = 8.394913061

Simplifying
y = 8.394913061


Subproblem 2
y + -2.5 = -5.894913061

Simplifying
y + -2.5 = -5.894913061

Reorder the terms:
-2.5 + y = -5.894913061

Solving
-2.5 + y = -5.894913061

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 = -5.894913061 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + y = -5.894913061 + 2.5
y = -5.894913061 + 2.5

Combine like terms: -5.894913061 + 2.5 = -3.394913061
y = -3.394913061

Simplifying
y = -3.394913061


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {8.394913061, -3.394913061}

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