3y+y^2=2

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Solution for 3y+y^2=2 equation:


Simplifying
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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