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Simplifying 9w2 = 12w + 5 Reorder the terms: 9w2 = 5 + 12w Solving 9w2 = 5 + 12w Solving for variable 'w'. Reorder the terms: -5 + -12w + 9w2 = 5 + 12w + -5 + -12w Reorder the terms: -5 + -12w + 9w2 = 5 + -5 + 12w + -12w Combine like terms: 5 + -5 = 0 -5 + -12w + 9w2 = 0 + 12w + -12w -5 + -12w + 9w2 = 12w + -12w Combine like terms: 12w + -12w = 0 -5 + -12w + 9w2 = 0 Factor a trinomial. (-1 + -3w)(5 + -3w) = 0Subproblem 1
Set the factor '(-1 + -3w)' equal to zero and attempt to solve: Simplifying -1 + -3w = 0 Solving -1 + -3w = 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 + -3w = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3w = 0 + 1 -3w = 0 + 1 Combine like terms: 0 + 1 = 1 -3w = 1 Divide each side by '-3'. w = -0.3333333333 Simplifying w = -0.3333333333Subproblem 2
Set the factor '(5 + -3w)' equal to zero and attempt to solve: Simplifying 5 + -3w = 0 Solving 5 + -3w = 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 + -3w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3w = 0 + -5 -3w = 0 + -5 Combine like terms: 0 + -5 = -5 -3w = -5 Divide each side by '-3'. w = 1.666666667 Simplifying w = 1.666666667Solution
w = {-0.3333333333, 1.666666667}
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