.25y^2-.75y-1=0

Solution for .25y^2-.75y-1=0 equation:

Simplifying
0.25y2 + -0.75y + -1 = 0

Reorder the terms:
-1 + -0.75y + 0.25y2 = 0

Solving
-1 + -0.75y + 0.25y2 = 0

Solving for variable 'y'.

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

Divide each side by '0.25'.
-4 + -3y + y2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -3y + 4 + y2 = 0 + 4

Reorder the terms:
-4 + 4 + -3y + y2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3y + y2 = 0 + 4
-3y + y2 = 0 + 4

Combine like terms: 0 + 4 = 4
-3y + y2 = 4

The y term is -3y.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3y + 2.25 + y2 = 4 + 2.25

Reorder the terms:
2.25 + -3y + y2 = 4 + 2.25

Combine like terms: 4 + 2.25 = 6.25
2.25 + -3y + y2 = 6.25

Factor a perfect square on the left side:
(y + -1.5)(y + -1.5) = 6.25

Calculate the square root of the right side: 2.5

Break this problem into two subproblems by setting 
(y + -1.5) equal to 2.5 and -2.5.

Subproblem 1
y + -1.5 = 2.5

Simplifying
y + -1.5 = 2.5

Reorder the terms:
-1.5 + y = 2.5

Solving
-1.5 + y = 2.5

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = 2.5 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = 2.5 + 1.5
y = 2.5 + 1.5

Combine like terms: 2.5 + 1.5 = 4
y = 4

Simplifying
y = 4

Subproblem 2
y + -1.5 = -2.5

Simplifying
y + -1.5 = -2.5

Reorder the terms:
-1.5 + y = -2.5

Solving
-1.5 + y = -2.5

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = -2.5 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = -2.5 + 1.5
y = -2.5 + 1.5

Combine like terms: -2.5 + 1.5 = -1
y = -1

Simplifying
y = -1

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4, -1}