y^2+10y+2=0

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Solution for y^2+10y+2=0 equation:


Simplifying
y2 + 10y + 2 = 0

Reorder the terms:
2 + 10y + y2 = 0

Solving
2 + 10y + 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 + 10y + -2 + y2 = 0 + -2

Reorder the terms:
2 + -2 + 10y + y2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 10y + y2 = 0 + -2
10y + y2 = 0 + -2

Combine like terms: 0 + -2 = -2
10y + y2 = -2

The y term is 10y.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10y + 25 + y2 = -2 + 25

Reorder the terms:
25 + 10y + y2 = -2 + 25

Combine like terms: -2 + 25 = 23
25 + 10y + y2 = 23

Factor a perfect square on the left side:
(y + 5)(y + 5) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(y + 5) equal to 4.795831523 and -4.795831523.


Subproblem 1
y + 5 = 4.795831523

Simplifying
y + 5 = 4.795831523

Reorder the terms:
5 + y = 4.795831523

Solving
5 + y = 4.795831523

Solving for variable 'y'.

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

Add '-5' to each side of the equation.
5 + -5 + y = 4.795831523 + -5

Combine like terms: 5 + -5 = 0
0 + y = 4.795831523 + -5
y = 4.795831523 + -5

Combine like terms: 4.795831523 + -5 = -0.204168477
y = -0.204168477

Simplifying
y = -0.204168477


Subproblem 2
y + 5 = -4.795831523

Simplifying
y + 5 = -4.795831523

Reorder the terms:
5 + y = -4.795831523

Solving
5 + y = -4.795831523

Solving for variable 'y'.

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

Add '-5' to each side of the equation.
5 + -5 + y = -4.795831523 + -5

Combine like terms: 5 + -5 = 0
0 + y = -4.795831523 + -5
y = -4.795831523 + -5

Combine like terms: -4.795831523 + -5 = -9.795831523
y = -9.795831523

Simplifying
y = -9.795831523


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.204168477, -9.795831523}

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