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Simplifying 150 = w(w + 5) Reorder the terms: 150 = w(5 + w) 150 = (5 * w + w * w) 150 = (5w + w2) Solving 150 = 5w + w2 Solving for variable 'w'. Reorder the terms: 150 + -5w + -1w2 = 5w + -5w + w2 + -1w2 Combine like terms: 5w + -5w = 0 150 + -5w + -1w2 = 0 + w2 + -1w2 150 + -5w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 150 + -5w + -1w2 = 0 Factor a trinomial. (10 + -1w)(15 + w) = 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 + w)' equal to zero and attempt to solve: Simplifying 15 + w = 0 Solving 15 + w = 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 + w = 0 + -15 Combine like terms: 15 + -15 = 0 0 + w = 0 + -15 w = 0 + -15 Combine like terms: 0 + -15 = -15 w = -15 Simplifying w = -15Solution
w = {10, -15}
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