-11w-5=2w^2

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


Simplifying
-11w + -5 = 2w2

Reorder the terms:
-5 + -11w = 2w2

Solving
-5 + -11w = 2w2

Solving for variable 'w'.

Combine like terms: 2w2 + -2w2 = 0
-5 + -11w + -2w2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 11w + 2w2) = 0

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

Ignore the factor -1.

Subproblem 1

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

Subproblem 2

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

Solution

w = {-5, -0.5}

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