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Simplifying 9w2 = 30 + 39w Solving 9w2 = 30 + 39w Solving for variable 'w'. Reorder the terms: -30 + -39w + 9w2 = 30 + 39w + -30 + -39w Reorder the terms: -30 + -39w + 9w2 = 30 + -30 + 39w + -39w Combine like terms: 30 + -30 = 0 -30 + -39w + 9w2 = 0 + 39w + -39w -30 + -39w + 9w2 = 39w + -39w Combine like terms: 39w + -39w = 0 -30 + -39w + 9w2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-10 + -13w + 3w2) = 0 Factor a trinomial. 3((-2 + -3w)(5 + -1w)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + -3w)' equal to zero and attempt to solve: Simplifying -2 + -3w = 0 Solving -2 + -3w = 0 Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -3w = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3w = 0 + 2 -3w = 0 + 2 Combine like terms: 0 + 2 = 2 -3w = 2 Divide each side by '-3'. w = -0.6666666667 Simplifying w = -0.6666666667Subproblem 2
Set the factor '(5 + -1w)' equal to zero and attempt to solve: Simplifying 5 + -1w = 0 Solving 5 + -1w = 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 + -1w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1w = 0 + -5 -1w = 0 + -5 Combine like terms: 0 + -5 = -5 -1w = -5 Divide each side by '-1'. w = 5 Simplifying w = 5Solution
w = {-0.6666666667, 5}
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