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Simplifying 0 = 2w2 + -5w + -150 Reorder the terms: 0 = -150 + -5w + 2w2 Solving 0 = -150 + -5w + 2w2 Solving for variable 'w'. Combine like terms: 0 + 150 = 150 150 + 5w + -2w2 = -150 + -5w + 2w2 + 150 + 5w + -2w2 Reorder the terms: 150 + 5w + -2w2 = -150 + 150 + -5w + 5w + 2w2 + -2w2 Combine like terms: -150 + 150 = 0 150 + 5w + -2w2 = 0 + -5w + 5w + 2w2 + -2w2 150 + 5w + -2w2 = -5w + 5w + 2w2 + -2w2 Combine like terms: -5w + 5w = 0 150 + 5w + -2w2 = 0 + 2w2 + -2w2 150 + 5w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 150 + 5w + -2w2 = 0 Factor a trinomial. (10 + -1w)(15 + 2w) = 0Subproblem 1
Set the factor '(10 + -1w)' equal to zero and attempt to solve: Simplifying 10 + -1w = 0 Solving 10 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1w = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1w = 0 + -10 -1w = 0 + -10 Combine like terms: 0 + -10 = -10 -1w = -10 Divide each side by '-1'. w = 10 Simplifying w = 10Subproblem 2
Set the factor '(15 + 2w)' equal to zero and attempt to solve: Simplifying 15 + 2w = 0 Solving 15 + 2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + 2w = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 2w = 0 + -15 2w = 0 + -15 Combine like terms: 0 + -15 = -15 2w = -15 Divide each side by '2'. w = -7.5 Simplifying w = -7.5Solution
w = {10, -7.5}
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