y^2+10y+12=0

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Solution for y^2+10y+12=0 equation: 


Simplifying
y2 + 10y + 12 = 0

Reorder the terms:
12 + 10y + y2 = 0

Solving
12 + 10y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + 10y + -12 + y2 = 0 + -12

Reorder the terms:
12 + -12 + 10y + y2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + 10y + y2 = 0 + -12
10y + y2 = 0 + -12

Combine like terms: 0 + -12 = -12
10y + y2 = -12

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 = -12 + 25

Reorder the terms:
25 + 10y + y2 = -12 + 25

Combine like terms: -12 + 25 = 13
25 + 10y + y2 = 13

Factor a perfect square on the left side:
(y + 5)(y + 5) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(y + 5) equal to 3.605551275 and -3.605551275.


Subproblem 1
y + 5 = 3.605551275

Simplifying
y + 5 = 3.605551275

Reorder the terms:
5 + y = 3.605551275

Solving
5 + y = 3.605551275

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 = 3.605551275 + -5

Combine like terms: 5 + -5 = 0
0 + y = 3.605551275 + -5
y = 3.605551275 + -5

Combine like terms: 3.605551275 + -5 = -1.394448725
y = -1.394448725

Simplifying
y = -1.394448725


Subproblem 2
y + 5 = -3.605551275

Simplifying
y + 5 = -3.605551275

Reorder the terms:
5 + y = -3.605551275

Solving
5 + y = -3.605551275

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 = -3.605551275 + -5

Combine like terms: 5 + -5 = 0
0 + y = -3.605551275 + -5
y = -3.605551275 + -5

Combine like terms: -3.605551275 + -5 = -8.605551275
y = -8.605551275

Simplifying
y = -8.605551275


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-1.394448725, -8.605551275}

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