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Simplifying 18 = w(2w + 5) Reorder the terms: 18 = w(5 + 2w) 18 = (5 * w + 2w * w) 18 = (5w + 2w2) Solving 18 = 5w + 2w2 Solving for variable 'w'. Reorder the terms: 18 + -5w + -2w2 = 5w + -5w + 2w2 + -2w2 Combine like terms: 5w + -5w = 0 18 + -5w + -2w2 = 0 + 2w2 + -2w2 18 + -5w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 18 + -5w + -2w2 = 0 Factor a trinomial. (2 + -1w)(9 + 2w) = 0Subproblem 1
Set the factor '(2 + -1w)' equal to zero and attempt to solve: Simplifying 2 + -1w = 0 Solving 2 + -1w = 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 + -1w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1w = 0 + -2 -1w = 0 + -2 Combine like terms: 0 + -2 = -2 -1w = -2 Divide each side by '-1'. w = 2 Simplifying w = 2Subproblem 2
Set the factor '(9 + 2w)' equal to zero and attempt to solve: Simplifying 9 + 2w = 0 Solving 9 + 2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 2w = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2w = 0 + -9 2w = 0 + -9 Combine like terms: 0 + -9 = -9 2w = -9 Divide each side by '2'. w = -4.5 Simplifying w = -4.5Solution
w = {2, -4.5}
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