y^2+9y+5=0

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Solution for y^2+9y+5=0 equation:


Simplifying
y2 + 9y + 5 = 0

Reorder the terms:
5 + 9y + y2 = 0

Solving
5 + 9y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 9y + -5 + y2 = 0 + -5

Reorder the terms:
5 + -5 + 9y + y2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 9y + y2 = 0 + -5
9y + y2 = 0 + -5

Combine like terms: 0 + -5 = -5
9y + y2 = -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 = -5 + 20.25

Reorder the terms:
20.25 + 9y + y2 = -5 + 20.25

Combine like terms: -5 + 20.25 = 15.25
20.25 + 9y + y2 = 15.25

Factor a perfect square on the left side:
(y + 4.5)(y + 4.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(y + 4.5) equal to 3.905124838 and -3.905124838.

Subproblem 1

y + 4.5 = 3.905124838 Simplifying y + 4.5 = 3.905124838 Reorder the terms: 4.5 + y = 3.905124838 Solving 4.5 + y = 3.905124838 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 = 3.905124838 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + y = 3.905124838 + -4.5 y = 3.905124838 + -4.5 Combine like terms: 3.905124838 + -4.5 = -0.594875162 y = -0.594875162 Simplifying y = -0.594875162

Subproblem 2

y + 4.5 = -3.905124838 Simplifying y + 4.5 = -3.905124838 Reorder the terms: 4.5 + y = -3.905124838 Solving 4.5 + y = -3.905124838 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 = -3.905124838 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + y = -3.905124838 + -4.5 y = -3.905124838 + -4.5 Combine like terms: -3.905124838 + -4.5 = -8.405124838 y = -8.405124838 Simplifying y = -8.405124838

Solution

The solution to the problem is based on the solutions from the subproblems. y = {-0.594875162, -8.405124838}

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