2y^2=-11y-5

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Solution for 2y^2=-11y-5 equation:


Simplifying
2y2 = -11y + -5

Reorder the terms:
2y2 = -5 + -11y

Solving
2y2 = -5 + -11y

Solving for variable 'y'.

Reorder the terms:
5 + 11y + 2y2 = -5 + -11y + 5 + 11y

Reorder the terms:
5 + 11y + 2y2 = -5 + 5 + -11y + 11y

Combine like terms: -5 + 5 = 0
5 + 11y + 2y2 = 0 + -11y + 11y
5 + 11y + 2y2 = -11y + 11y

Combine like terms: -11y + 11y = 0
5 + 11y + 2y2 = 0

Factor a trinomial.
(5 + y)(1 + 2y) = 0

Subproblem 1

Set the factor '(5 + y)' equal to zero and attempt to solve: Simplifying 5 + y = 0 Solving 5 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + y = 0 + -5 y = 0 + -5 Combine like terms: 0 + -5 = -5 y = -5 Simplifying y = -5

Subproblem 2

Set the factor '(1 + 2y)' equal to zero and attempt to solve: Simplifying 1 + 2y = 0 Solving 1 + 2y = 0 Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2y = 0 + -1 2y = 0 + -1 Combine like terms: 0 + -1 = -1 2y = -1 Divide each side by '2'. y = -0.5 Simplifying y = -0.5

Solution

y = {-5, -0.5}

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