3y^2+6y-2=0

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Solution for 3y^2+6y-2=0 equation:


Simplifying
3y2 + 6y + -2 = 0

Reorder the terms:
-2 + 6y + 3y2 = 0

Solving
-2 + 6y + 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'.
-0.6666666667 + 2y + y2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + 2y + 0.6666666667 + y2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + 2y + y2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + 2y + y2 = 0 + 0.6666666667
2y + y2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
2y + y2 = 0.6666666667

The y term is 2y.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2y + 1 + y2 = 0.6666666667 + 1

Reorder the terms:
1 + 2y + y2 = 0.6666666667 + 1

Combine like terms: 0.6666666667 + 1 = 1.6666666667
1 + 2y + y2 = 1.6666666667

Factor a perfect square on the left side:
(y + 1)(y + 1) = 1.6666666667

Calculate the square root of the right side: 1.290994449

Break this problem into two subproblems by setting 
(y + 1) equal to 1.290994449 and -1.290994449.

Subproblem 1

y + 1 = 1.290994449 Simplifying y + 1 = 1.290994449 Reorder the terms: 1 + y = 1.290994449 Solving 1 + y = 1.290994449 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 1.290994449 + -1 Combine like terms: 1 + -1 = 0 0 + y = 1.290994449 + -1 y = 1.290994449 + -1 Combine like terms: 1.290994449 + -1 = 0.290994449 y = 0.290994449 Simplifying y = 0.290994449

Subproblem 2

y + 1 = -1.290994449 Simplifying y + 1 = -1.290994449 Reorder the terms: 1 + y = -1.290994449 Solving 1 + y = -1.290994449 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = -1.290994449 + -1 Combine like terms: 1 + -1 = 0 0 + y = -1.290994449 + -1 y = -1.290994449 + -1 Combine like terms: -1.290994449 + -1 = -2.290994449 y = -2.290994449 Simplifying y = -2.290994449

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.290994449, -2.290994449}

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