2y^2+17y+20=0

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Solution for 2y^2+17y+20=0 equation:


Simplifying
2y2 + 17y + 20 = 0

Reorder the terms:
20 + 17y + 2y2 = 0

Solving
20 + 17y + 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'.
10 + 8.5y + y2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 8.5y + -10 + y2 = 0 + -10

Reorder the terms:
10 + -10 + 8.5y + y2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 8.5y + y2 = 0 + -10
8.5y + y2 = 0 + -10

Combine like terms: 0 + -10 = -10
8.5y + y2 = -10

The y term is 8.5y.  Take half its coefficient (4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
8.5y + 18.0625 + y2 = -10 + 18.0625

Reorder the terms:
18.0625 + 8.5y + y2 = -10 + 18.0625

Combine like terms: -10 + 18.0625 = 8.0625
18.0625 + 8.5y + y2 = 8.0625

Factor a perfect square on the left side:
(y + 4.25)(y + 4.25) = 8.0625

Calculate the square root of the right side: 2.839454173

Break this problem into two subproblems by setting 
(y + 4.25) equal to 2.839454173 and -2.839454173.

Subproblem 1

y + 4.25 = 2.839454173 Simplifying y + 4.25 = 2.839454173 Reorder the terms: 4.25 + y = 2.839454173 Solving 4.25 + y = 2.839454173 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + y = 2.839454173 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + y = 2.839454173 + -4.25 y = 2.839454173 + -4.25 Combine like terms: 2.839454173 + -4.25 = -1.410545827 y = -1.410545827 Simplifying y = -1.410545827

Subproblem 2

y + 4.25 = -2.839454173 Simplifying y + 4.25 = -2.839454173 Reorder the terms: 4.25 + y = -2.839454173 Solving 4.25 + y = -2.839454173 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + y = -2.839454173 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + y = -2.839454173 + -4.25 y = -2.839454173 + -4.25 Combine like terms: -2.839454173 + -4.25 = -7.089454173 y = -7.089454173 Simplifying y = -7.089454173

Solution

The solution to the problem is based on the solutions from the subproblems. y = {-1.410545827, -7.089454173}

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