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