y^2+6y+2=0

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Solution for y^2+6y+2=0 equation:


Simplifying
y2 + 6y + 2 = 0

Reorder the terms:
2 + 6y + y2 = 0

Solving
2 + 6y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 6y + -2 + y2 = 0 + -2

Reorder the terms:
2 + -2 + 6y + y2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 6y + y2 = 0 + -2
6y + y2 = 0 + -2

Combine like terms: 0 + -2 = -2
6y + y2 = -2

The y term is 6y.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6y + 9 + y2 = -2 + 9

Reorder the terms:
9 + 6y + y2 = -2 + 9

Combine like terms: -2 + 9 = 7
9 + 6y + y2 = 7

Factor a perfect square on the left side:
(y + 3)(y + 3) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(y + 3) equal to 2.645751311 and -2.645751311.


Subproblem 1
y + 3 = 2.645751311

Simplifying
y + 3 = 2.645751311

Reorder the terms:
3 + y = 2.645751311

Solving
3 + y = 2.645751311

Solving for variable 'y'.

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

Add '-3' to each side of the equation.
3 + -3 + y = 2.645751311 + -3

Combine like terms: 3 + -3 = 0
0 + y = 2.645751311 + -3
y = 2.645751311 + -3

Combine like terms: 2.645751311 + -3 = -0.354248689
y = -0.354248689

Simplifying
y = -0.354248689


Subproblem 2
y + 3 = -2.645751311

Simplifying
y + 3 = -2.645751311

Reorder the terms:
3 + y = -2.645751311

Solving
3 + y = -2.645751311

Solving for variable 'y'.

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

Add '-3' to each side of the equation.
3 + -3 + y = -2.645751311 + -3

Combine like terms: 3 + -3 = 0
0 + y = -2.645751311 + -3
y = -2.645751311 + -3

Combine like terms: -2.645751311 + -3 = -5.645751311
y = -5.645751311

Simplifying
y = -5.645751311


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.354248689, -5.645751311}

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