y^2+y=2.5

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Solution for y^2+y=2.5 equation: 


Simplifying
y2 + y = 2.5

Reorder the terms:
y + y2 = 2.5

Solving
y + y2 = 2.5

Solving for variable 'y'.

Reorder the terms:
-2.5 + y + y2 = 2.5 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
-2.5 + y + y2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + y + 2.5 + y2 = 0.0 + 2.5

Reorder the terms:
-2.5 + 2.5 + y + y2 = 0.0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + y + y2 = 0.0 + 2.5
y + y2 = 0.0 + 2.5

Combine like terms: 0.0 + 2.5 = 2.5
y + y2 = 2.5

The y term is y.  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 = 2.5 + 0.25

Reorder the terms:
0.25 + y + y2 = 2.5 + 0.25

Combine like terms: 2.5 + 0.25 = 2.75
0.25 + y + y2 = 2.75

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(y + 0.5) equal to 1.658312395 and -1.658312395.


Subproblem 1
y + 0.5 = 1.658312395

Simplifying
y + 0.5 = 1.658312395

Reorder the terms:
0.5 + y = 1.658312395

Solving
0.5 + y = 1.658312395

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 = 1.658312395 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = 1.658312395 + -0.5
y = 1.658312395 + -0.5

Combine like terms: 1.658312395 + -0.5 = 1.158312395
y = 1.158312395

Simplifying
y = 1.158312395


Subproblem 2
y + 0.5 = -1.658312395

Simplifying
y + 0.5 = -1.658312395

Reorder the terms:
0.5 + y = -1.658312395

Solving
0.5 + y = -1.658312395

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 = -1.658312395 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = -1.658312395 + -0.5
y = -1.658312395 + -0.5

Combine like terms: -1.658312395 + -0.5 = -2.158312395
y = -2.158312395

Simplifying
y = -2.158312395


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.158312395, -2.158312395}

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