11v=-30-v^2

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Solution for 11v=-30-v^2 equation:


Simplifying
11v = -30 + -1v2

Solving
11v = -30 + -1v2

Solving for variable 'v'.

Reorder the terms:
30 + 11v + v2 = -30 + -1v2 + 30 + v2

Reorder the terms:
30 + 11v + v2 = -30 + 30 + -1v2 + v2

Combine like terms: -30 + 30 = 0
30 + 11v + v2 = 0 + -1v2 + v2
30 + 11v + v2 = -1v2 + v2

Combine like terms: -1v2 + v2 = 0
30 + 11v + v2 = 0

Factor a trinomial.
(6 + v)(5 + v) = 0

Subproblem 1

Set the factor '(6 + v)' equal to zero and attempt to solve: Simplifying 6 + v = 0 Solving 6 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + v = 0 + -6 Combine like terms: 6 + -6 = 0 0 + v = 0 + -6 v = 0 + -6 Combine like terms: 0 + -6 = -6 v = -6 Simplifying v = -6

Subproblem 2

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

Solution

v = {-6, -5}

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