y+y^2=2.16

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Solution for y+y^2=2.16 equation: 


Simplifying
y + y2 = 2.16

Solving
y + y2 = 2.16

Solving for variable 'y'.

Reorder the terms:
-2.16 + y + y2 = 2.16 + -2.16

Combine like terms: 2.16 + -2.16 = 0.00
-2.16 + y + y2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '2.16' to each side of the equation.
-2.16 + y + 2.16 + y2 = 0.00 + 2.16

Reorder the terms:
-2.16 + 2.16 + y + y2 = 0.00 + 2.16

Combine like terms: -2.16 + 2.16 = 0.00
0.00 + y + y2 = 0.00 + 2.16
y + y2 = 0.00 + 2.16

Combine like terms: 0.00 + 2.16 = 2.16
y + y2 = 2.16

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 = 2.16 + 0.25

Reorder the terms:
0.25 + y + y2 = 2.16 + 0.25

Combine like terms: 2.16 + 0.25 = 2.41
0.25 + y + y2 = 2.41

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 2.41

Calculate the square root of the right side: 1.55241747

Break this problem into two subproblems by setting 
(y + 0.5) equal to 1.55241747 and -1.55241747.


Subproblem 1
y + 0.5 = 1.55241747

Simplifying
y + 0.5 = 1.55241747

Reorder the terms:
0.5 + y = 1.55241747

Solving
0.5 + y = 1.55241747

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 = 1.55241747 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = 1.55241747 + -0.5
y = 1.55241747 + -0.5

Combine like terms: 1.55241747 + -0.5 = 1.05241747
y = 1.05241747

Simplifying
y = 1.05241747


Subproblem 2
y + 0.5 = -1.55241747

Simplifying
y + 0.5 = -1.55241747

Reorder the terms:
0.5 + y = -1.55241747

Solving
0.5 + y = -1.55241747

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 = -1.55241747 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = -1.55241747 + -0.5
y = -1.55241747 + -0.5

Combine like terms: -1.55241747 + -0.5 = -2.05241747
y = -2.05241747

Simplifying
y = -2.05241747


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.05241747, -2.05241747}

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