y(y+3)=2

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Solution for y(y+3)=2 equation: 


Simplifying
y(y + 3) = 2

Reorder the terms:
y(3 + y) = 2
(3 * y + y * y) = 2
(3y + y2) = 2

Solving
3y + y2 = 2

Solving for variable 'y'.

Reorder the terms:
-2 + 3y + y2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 3y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 3y + 2 + y2 = 0 + 2

Reorder the terms:
-2 + 2 + 3y + y2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 3y + y2 = 0 + 2
3y + y2 = 0 + 2

Combine like terms: 0 + 2 = 2
3y + y2 = 2

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 = 2 + 2.25

Reorder the terms:
2.25 + 3y + y2 = 2 + 2.25

Combine like terms: 2 + 2.25 = 4.25
2.25 + 3y + y2 = 4.25

Factor a perfect square on the left side:
(y + 1.5)(y + 1.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(y + 1.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
y + 1.5 = 2.061552813

Simplifying
y + 1.5 = 2.061552813

Reorder the terms:
1.5 + y = 2.061552813

Solving
1.5 + y = 2.061552813

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 = 2.061552813 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = 2.061552813 + -1.5
y = 2.061552813 + -1.5

Combine like terms: 2.061552813 + -1.5 = 0.561552813
y = 0.561552813

Simplifying
y = 0.561552813


Subproblem 2
y + 1.5 = -2.061552813

Simplifying
y + 1.5 = -2.061552813

Reorder the terms:
1.5 + y = -2.061552813

Solving
1.5 + y = -2.061552813

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 = -2.061552813 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = -2.061552813 + -1.5
y = -2.061552813 + -1.5

Combine like terms: -2.061552813 + -1.5 = -3.561552813
y = -3.561552813

Simplifying
y = -3.561552813


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.561552813, -3.561552813}

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