y^2+9y+7=0

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Solution for y^2+9y+7=0 equation: 


Simplifying
y2 + 9y + 7 = 0

Reorder the terms:
7 + 9y + y2 = 0

Solving
7 + 9y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 9y + -7 + y2 = 0 + -7

Reorder the terms:
7 + -7 + 9y + y2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 9y + y2 = 0 + -7
9y + y2 = 0 + -7

Combine like terms: 0 + -7 = -7
9y + y2 = -7

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 = -7 + 20.25

Reorder the terms:
20.25 + 9y + y2 = -7 + 20.25

Combine like terms: -7 + 20.25 = 13.25
20.25 + 9y + y2 = 13.25

Factor a perfect square on the left side:
(y + 4.5)(y + 4.5) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(y + 4.5) equal to 3.640054945 and -3.640054945.


Subproblem 1
y + 4.5 = 3.640054945

Simplifying
y + 4.5 = 3.640054945

Reorder the terms:
4.5 + y = 3.640054945

Solving
4.5 + y = 3.640054945

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 = 3.640054945 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + y = 3.640054945 + -4.5
y = 3.640054945 + -4.5

Combine like terms: 3.640054945 + -4.5 = -0.859945055
y = -0.859945055

Simplifying
y = -0.859945055


Subproblem 2
y + 4.5 = -3.640054945

Simplifying
y + 4.5 = -3.640054945

Reorder the terms:
4.5 + y = -3.640054945

Solving
4.5 + y = -3.640054945

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 = -3.640054945 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + y = -3.640054945 + -4.5
y = -3.640054945 + -4.5

Combine like terms: -3.640054945 + -4.5 = -8.140054945
y = -8.140054945

Simplifying
y = -8.140054945


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.859945055, -8.140054945}

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