2y^2+6y-27=0

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Solution for 2y^2+6y-27=0 equation:


Simplifying
2y2 + 6y + -27 = 0

Reorder the terms:
-27 + 6y + 2y2 = 0

Solving
-27 + 6y + 2y2 = 0

Solving for variable 'y'.

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

Divide each side by '2'.
-13.5 + 3y + y2 = 0

Move the constant term to the right:

Add '13.5' to each side of the equation.
-13.5 + 3y + 13.5 + y2 = 0 + 13.5

Reorder the terms:
-13.5 + 13.5 + 3y + y2 = 0 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + 3y + y2 = 0 + 13.5
3y + y2 = 0 + 13.5

Combine like terms: 0 + 13.5 = 13.5
3y + y2 = 13.5

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 = 13.5 + 2.25

Reorder the terms:
2.25 + 3y + y2 = 13.5 + 2.25

Combine like terms: 13.5 + 2.25 = 15.75
2.25 + 3y + y2 = 15.75

Factor a perfect square on the left side:
(y + 1.5)(y + 1.5) = 15.75

Calculate the square root of the right side: 3.968626967

Break this problem into two subproblems by setting 
(y + 1.5) equal to 3.968626967 and -3.968626967.

Subproblem 1

y + 1.5 = 3.968626967 Simplifying y + 1.5 = 3.968626967 Reorder the terms: 1.5 + y = 3.968626967 Solving 1.5 + y = 3.968626967 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 = 3.968626967 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = 3.968626967 + -1.5 y = 3.968626967 + -1.5 Combine like terms: 3.968626967 + -1.5 = 2.468626967 y = 2.468626967 Simplifying y = 2.468626967

Subproblem 2

y + 1.5 = -3.968626967 Simplifying y + 1.5 = -3.968626967 Reorder the terms: 1.5 + y = -3.968626967 Solving 1.5 + y = -3.968626967 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 = -3.968626967 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = -3.968626967 + -1.5 y = -3.968626967 + -1.5 Combine like terms: -3.968626967 + -1.5 = -5.468626967 y = -5.468626967 Simplifying y = -5.468626967

Solution

The solution to the problem is based on the solutions from the subproblems. y = {2.468626967, -5.468626967}

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