y^2-0.75y=0.25

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Solution for y^2-0.75y=0.25 equation: 


Simplifying
y2 + -0.75y = 0.25

Reorder the terms:
-0.75y + y2 = 0.25

Solving
-0.75y + y2 = 0.25

Solving for variable 'y'.

Reorder the terms:
-0.25 + -0.75y + y2 = 0.25 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
-0.25 + -0.75y + y2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -0.75y + 0.25 + y2 = 0.00 + 0.25

Reorder the terms:
-0.25 + 0.25 + -0.75y + y2 = 0.00 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -0.75y + y2 = 0.00 + 0.25
-0.75y + y2 = 0.00 + 0.25

Combine like terms: 0.00 + 0.25 = 0.25
-0.75y + y2 = 0.25

The y term is -0.75y.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75y + 0.140625 + y2 = 0.25 + 0.140625

Reorder the terms:
0.140625 + -0.75y + y2 = 0.25 + 0.140625

Combine like terms: 0.25 + 0.140625 = 0.390625
0.140625 + -0.75y + y2 = 0.390625

Factor a perfect square on the left side:
(y + -0.375)(y + -0.375) = 0.390625

Calculate the square root of the right side: 0.625

Break this problem into two subproblems by setting 
(y + -0.375) equal to 0.625 and -0.625.


Subproblem 1
y + -0.375 = 0.625

Simplifying
y + -0.375 = 0.625

Reorder the terms:
-0.375 + y = 0.625

Solving
-0.375 + y = 0.625

Solving for variable 'y'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + y = 0.625 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + y = 0.625 + 0.375
y = 0.625 + 0.375

Combine like terms: 0.625 + 0.375 = 1
y = 1

Simplifying
y = 1


Subproblem 2
y + -0.375 = -0.625

Simplifying
y + -0.375 = -0.625

Reorder the terms:
-0.375 + y = -0.625

Solving
-0.375 + y = -0.625

Solving for variable 'y'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + y = -0.625 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + y = -0.625 + 0.375
y = -0.625 + 0.375

Combine like terms: -0.625 + 0.375 = -0.25
y = -0.25

Simplifying
y = -0.25


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1, -0.25}

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