y*(y-25)=-101.25

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Solution for y*(y-25)=-101.25 equation: 


Simplifying
y(y + -25) = -101.25

Reorder the terms:
y(-25 + y) = -101.25
(-25 * y + y * y) = -101.25
(-25y + y2) = -101.25

Solving
-25y + y2 = -101.25

Solving for variable 'y'.

Reorder the terms:
101.25 + -25y + y2 = -101.25 + 101.25

Combine like terms: -101.25 + 101.25 = 0.00
101.25 + -25y + y2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '-101.25' to each side of the equation.
101.25 + -25y + -101.25 + y2 = 0.00 + -101.25

Reorder the terms:
101.25 + -101.25 + -25y + y2 = 0.00 + -101.25

Combine like terms: 101.25 + -101.25 = 0.00
0.00 + -25y + y2 = 0.00 + -101.25
-25y + y2 = 0.00 + -101.25

Combine like terms: 0.00 + -101.25 = -101.25
-25y + y2 = -101.25

The y term is -25y.  Take half its coefficient (-12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
-25y + 156.25 + y2 = -101.25 + 156.25

Reorder the terms:
156.25 + -25y + y2 = -101.25 + 156.25

Combine like terms: -101.25 + 156.25 = 55
156.25 + -25y + y2 = 55

Factor a perfect square on the left side:
(y + -12.5)(y + -12.5) = 55

Calculate the square root of the right side: 7.416198487

Break this problem into two subproblems by setting 
(y + -12.5) equal to 7.416198487 and -7.416198487.


Subproblem 1
y + -12.5 = 7.416198487

Simplifying
y + -12.5 = 7.416198487

Reorder the terms:
-12.5 + y = 7.416198487

Solving
-12.5 + y = 7.416198487

Solving for variable 'y'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + y = 7.416198487 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + y = 7.416198487 + 12.5
y = 7.416198487 + 12.5

Combine like terms: 7.416198487 + 12.5 = 19.916198487
y = 19.916198487

Simplifying
y = 19.916198487


Subproblem 2
y + -12.5 = -7.416198487

Simplifying
y + -12.5 = -7.416198487

Reorder the terms:
-12.5 + y = -7.416198487

Solving
-12.5 + y = -7.416198487

Solving for variable 'y'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + y = -7.416198487 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + y = -7.416198487 + 12.5
y = -7.416198487 + 12.5

Combine like terms: -7.416198487 + 12.5 = 5.083801513
y = 5.083801513

Simplifying
y = 5.083801513


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {19.916198487, 5.083801513}

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