y^2+3y-16=0

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Solution for y^2+3y-16=0 equation: 


Simplifying
y2 + 3y + -16 = 0

Reorder the terms:
-16 + 3y + y2 = 0

Solving
-16 + 3y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 3y + 16 + y2 = 0 + 16

Reorder the terms:
-16 + 16 + 3y + y2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 3y + y2 = 0 + 16
3y + y2 = 0 + 16

Combine like terms: 0 + 16 = 16
3y + y2 = 16

The y term is 3y.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3y + 2.25 + y2 = 16 + 2.25

Reorder the terms:
2.25 + 3y + y2 = 16 + 2.25

Combine like terms: 16 + 2.25 = 18.25
2.25 + 3y + y2 = 18.25

Factor a perfect square on the left side:
(y + 1.5)(y + 1.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(y + 1.5) equal to 4.272001873 and -4.272001873.


Subproblem 1
y + 1.5 = 4.272001873

Simplifying
y + 1.5 = 4.272001873

Reorder the terms:
1.5 + y = 4.272001873

Solving
1.5 + y = 4.272001873

Solving for variable 'y'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + y = 4.272001873 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = 4.272001873 + -1.5
y = 4.272001873 + -1.5

Combine like terms: 4.272001873 + -1.5 = 2.772001873
y = 2.772001873

Simplifying
y = 2.772001873


Subproblem 2
y + 1.5 = -4.272001873

Simplifying
y + 1.5 = -4.272001873

Reorder the terms:
1.5 + y = -4.272001873

Solving
1.5 + y = -4.272001873

Solving for variable 'y'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + y = -4.272001873 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = -4.272001873 + -1.5
y = -4.272001873 + -1.5

Combine like terms: -4.272001873 + -1.5 = -5.772001873
y = -5.772001873

Simplifying
y = -5.772001873


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.772001873, -5.772001873}

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