y^2-9y+15=0

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Solution for y^2-9y+15=0 equation: 


Simplifying
y2 + -9y + 15 = 0

Reorder the terms:
15 + -9y + y2 = 0

Solving
15 + -9y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + -9y + -15 + y2 = 0 + -15

Reorder the terms:
15 + -15 + -9y + y2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -9y + y2 = 0 + -15
-9y + y2 = 0 + -15

Combine like terms: 0 + -15 = -15
-9y + y2 = -15

The y term is -9y.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9y + 20.25 + y2 = -15 + 20.25

Reorder the terms:
20.25 + -9y + y2 = -15 + 20.25

Combine like terms: -15 + 20.25 = 5.25
20.25 + -9y + y2 = 5.25

Factor a perfect square on the left side:
(y + -4.5)(y + -4.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(y + -4.5) equal to 2.291287847 and -2.291287847.


Subproblem 1
y + -4.5 = 2.291287847

Simplifying
y + -4.5 = 2.291287847

Reorder the terms:
-4.5 + y = 2.291287847

Solving
-4.5 + y = 2.291287847

Solving for variable 'y'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + y = 2.291287847 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + y = 2.291287847 + 4.5
y = 2.291287847 + 4.5

Combine like terms: 2.291287847 + 4.5 = 6.791287847
y = 6.791287847

Simplifying
y = 6.791287847


Subproblem 2
y + -4.5 = -2.291287847

Simplifying
y + -4.5 = -2.291287847

Reorder the terms:
-4.5 + y = -2.291287847

Solving
-4.5 + y = -2.291287847

Solving for variable 'y'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + y = -2.291287847 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + y = -2.291287847 + 4.5
y = -2.291287847 + 4.5

Combine like terms: -2.291287847 + 4.5 = 2.208712153
y = 2.208712153

Simplifying
y = 2.208712153


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {6.791287847, 2.208712153}

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