y^2+9y=26.50

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Solution for y^2+9y=26.50 equation: 


Simplifying
y2 + 9y = 26.50

Reorder the terms:
9y + y2 = 26.50

Solving
9y + y2 = 26.50

Solving for variable 'y'.

Reorder the terms:
-26.50 + 9y + y2 = 26.50 + -26.50

Combine like terms: 26.50 + -26.50 = 0.00
-26.50 + 9y + y2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '26.50' to each side of the equation.
-26.50 + 9y + 26.50 + y2 = 0.00 + 26.50

Reorder the terms:
-26.50 + 26.50 + 9y + y2 = 0.00 + 26.50

Combine like terms: -26.50 + 26.50 = 0.00
0.00 + 9y + y2 = 0.00 + 26.50
9y + y2 = 0.00 + 26.50

Combine like terms: 0.00 + 26.50 = 26.5
9y + y2 = 26.5

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 = 26.5 + 20.25

Reorder the terms:
20.25 + 9y + y2 = 26.5 + 20.25

Combine like terms: 26.5 + 20.25 = 46.75
20.25 + 9y + y2 = 46.75

Factor a perfect square on the left side:
(y + 4.5)(y + 4.5) = 46.75

Calculate the square root of the right side: 6.837397166

Break this problem into two subproblems by setting 
(y + 4.5) equal to 6.837397166 and -6.837397166.


Subproblem 1
y + 4.5 = 6.837397166

Simplifying
y + 4.5 = 6.837397166

Reorder the terms:
4.5 + y = 6.837397166

Solving
4.5 + y = 6.837397166

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 = 6.837397166 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + y = 6.837397166 + -4.5
y = 6.837397166 + -4.5

Combine like terms: 6.837397166 + -4.5 = 2.337397166
y = 2.337397166

Simplifying
y = 2.337397166


Subproblem 2
y + 4.5 = -6.837397166

Simplifying
y + 4.5 = -6.837397166

Reorder the terms:
4.5 + y = -6.837397166

Solving
4.5 + y = -6.837397166

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 = -6.837397166 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + y = -6.837397166 + -4.5
y = -6.837397166 + -4.5

Combine like terms: -6.837397166 + -4.5 = -11.337397166
y = -11.337397166

Simplifying
y = -11.337397166


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.337397166, -11.337397166}

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