3y^2+21y+26=0

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Solution for 3y^2+21y+26=0 equation: 


Simplifying
3y2 + 21y + 26 = 0

Reorder the terms:
26 + 21y + 3y2 = 0

Solving
26 + 21y + 3y2 = 0

Solving for variable 'y'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
8.666666667 + 7y + y2 = 0

Move the constant term to the right:

Add '-8.666666667' to each side of the equation.
8.666666667 + 7y + -8.666666667 + y2 = 0 + -8.666666667

Reorder the terms:
8.666666667 + -8.666666667 + 7y + y2 = 0 + -8.666666667

Combine like terms: 8.666666667 + -8.666666667 = 0.000000000
0.000000000 + 7y + y2 = 0 + -8.666666667
7y + y2 = 0 + -8.666666667

Combine like terms: 0 + -8.666666667 = -8.666666667
7y + y2 = -8.666666667

The y term is 7y.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7y + 12.25 + y2 = -8.666666667 + 12.25

Reorder the terms:
12.25 + 7y + y2 = -8.666666667 + 12.25

Combine like terms: -8.666666667 + 12.25 = 3.583333333
12.25 + 7y + y2 = 3.583333333

Factor a perfect square on the left side:
(y + 3.5)(y + 3.5) = 3.583333333

Calculate the square root of the right side: 1.892969449

Break this problem into two subproblems by setting 
(y + 3.5) equal to 1.892969449 and -1.892969449.


Subproblem 1
y + 3.5 = 1.892969449

Simplifying
y + 3.5 = 1.892969449

Reorder the terms:
3.5 + y = 1.892969449

Solving
3.5 + y = 1.892969449

Solving for variable 'y'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + y = 1.892969449 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + y = 1.892969449 + -3.5
y = 1.892969449 + -3.5

Combine like terms: 1.892969449 + -3.5 = -1.607030551
y = -1.607030551

Simplifying
y = -1.607030551


Subproblem 2
y + 3.5 = -1.892969449

Simplifying
y + 3.5 = -1.892969449

Reorder the terms:
3.5 + y = -1.892969449

Solving
3.5 + y = -1.892969449

Solving for variable 'y'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + y = -1.892969449 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + y = -1.892969449 + -3.5
y = -1.892969449 + -3.5

Combine like terms: -1.892969449 + -3.5 = -5.392969449
y = -5.392969449

Simplifying
y = -5.392969449


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-1.607030551, -5.392969449}

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