2y^2+3y-15=0

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Solution for 2y^2+3y-15=0 equation:


Simplifying
2y2 + 3y + -15 = 0

Reorder the terms:
-15 + 3y + 2y2 = 0

Solving
-15 + 3y + 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'.
-7.5 + 1.5y + y2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + 1.5y + 7.5 + y2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + 1.5y + y2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + 1.5y + y2 = 0 + 7.5
1.5y + y2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
1.5y + y2 = 7.5

The y term is 1.5y.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5y + 0.5625 + y2 = 7.5 + 0.5625

Reorder the terms:
0.5625 + 1.5y + y2 = 7.5 + 0.5625

Combine like terms: 7.5 + 0.5625 = 8.0625
0.5625 + 1.5y + y2 = 8.0625

Factor a perfect square on the left side:
(y + 0.75)(y + 0.75) = 8.0625

Calculate the square root of the right side: 2.839454173

Break this problem into two subproblems by setting 
(y + 0.75) equal to 2.839454173 and -2.839454173.

Subproblem 1

y + 0.75 = 2.839454173 Simplifying y + 0.75 = 2.839454173 Reorder the terms: 0.75 + y = 2.839454173 Solving 0.75 + y = 2.839454173 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + y = 2.839454173 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + y = 2.839454173 + -0.75 y = 2.839454173 + -0.75 Combine like terms: 2.839454173 + -0.75 = 2.089454173 y = 2.089454173 Simplifying y = 2.089454173

Subproblem 2

y + 0.75 = -2.839454173 Simplifying y + 0.75 = -2.839454173 Reorder the terms: 0.75 + y = -2.839454173 Solving 0.75 + y = -2.839454173 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + y = -2.839454173 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + y = -2.839454173 + -0.75 y = -2.839454173 + -0.75 Combine like terms: -2.839454173 + -0.75 = -3.589454173 y = -3.589454173 Simplifying y = -3.589454173

Solution

The solution to the problem is based on the solutions from the subproblems. y = {2.089454173, -3.589454173}

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