y^2+y-9=0

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Solution for y^2+y-9=0 equation: 


Simplifying
y2 + y + -9 = 0

Reorder the terms:
-9 + y + y2 = 0

Solving
-9 + y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + y + 9 + y2 = 0 + 9

Reorder the terms:
-9 + 9 + y + y2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + y + y2 = 0 + 9
y + y2 = 0 + 9

Combine like terms: 0 + 9 = 9
y + y2 = 9

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 = 9 + 0.25

Reorder the terms:
0.25 + y + y2 = 9 + 0.25

Combine like terms: 9 + 0.25 = 9.25
0.25 + y + y2 = 9.25

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(y + 0.5) equal to 3.041381265 and -3.041381265.


Subproblem 1
y + 0.5 = 3.041381265

Simplifying
y + 0.5 = 3.041381265

Reorder the terms:
0.5 + y = 3.041381265

Solving
0.5 + y = 3.041381265

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 = 3.041381265 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = 3.041381265 + -0.5
y = 3.041381265 + -0.5

Combine like terms: 3.041381265 + -0.5 = 2.541381265
y = 2.541381265

Simplifying
y = 2.541381265


Subproblem 2
y + 0.5 = -3.041381265

Simplifying
y + 0.5 = -3.041381265

Reorder the terms:
0.5 + y = -3.041381265

Solving
0.5 + y = -3.041381265

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 = -3.041381265 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = -3.041381265 + -0.5
y = -3.041381265 + -0.5

Combine like terms: -3.041381265 + -0.5 = -3.541381265
y = -3.541381265

Simplifying
y = -3.541381265


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.541381265, -3.541381265}

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