y(y+1)=0.75

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Solution for y(y+1)=0.75 equation: 


Simplifying
y(y + 1) = 0.75

Reorder the terms:
y(1 + y) = 0.75
(1 * y + y * y) = 0.75
(1y + y2) = 0.75

Solving
1y + y2 = 0.75

Solving for variable 'y'.

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

Combine like terms: 0.75 + -0.75 = 0.00
-0.75 + 1y + y2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + 1y + 0.75 + y2 = 0.00 + 0.75

Reorder the terms:
-0.75 + 0.75 + 1y + y2 = 0.00 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + 1y + y2 = 0.00 + 0.75
1y + y2 = 0.00 + 0.75

Combine like terms: 0.00 + 0.75 = 0.75
1y + y2 = 0.75

The y term is 1y.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

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

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

Combine like terms: 0.75 + 0.25 = 1
0.25 + y + y2 = 1

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 1

Calculate the square root of the right side: 1

Break this problem into two subproblems by setting 
(y + 0.5) equal to 1 and -1.


Subproblem 1
y + 0.5 = 1

Simplifying
y + 0.5 = 1

Reorder the terms:
0.5 + y = 1

Solving
0.5 + y = 1

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = 1 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = 1 + -0.5
y = 1 + -0.5

Combine like terms: 1 + -0.5 = 0.5
y = 0.5

Simplifying
y = 0.5


Subproblem 2
y + 0.5 = -1

Simplifying
y + 0.5 = -1

Reorder the terms:
0.5 + y = -1

Solving
0.5 + y = -1

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = -1 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = -1 + -0.5
y = -1 + -0.5

Combine like terms: -1 + -0.5 = -1.5
y = -1.5

Simplifying
y = -1.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.5, -1.5}

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