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Simplifying 250 = w(2w + 5) Reorder the terms: 250 = w(5 + 2w) 250 = (5 * w + 2w * w) 250 = (5w + 2w2) Solving 250 = 5w + 2w2 Solving for variable 'w'. Reorder the terms: 250 + -5w + -2w2 = 5w + -5w + 2w2 + -2w2 Combine like terms: 5w + -5w = 0 250 + -5w + -2w2 = 0 + 2w2 + -2w2 250 + -5w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 250 + -5w + -2w2 = 0 Factor a trinomial. (10 + -1w)(25 + 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 '(25 + 2w)' equal to zero and attempt to solve: Simplifying 25 + 2w = 0 Solving 25 + 2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + 2w = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 2w = 0 + -25 2w = 0 + -25 Combine like terms: 0 + -25 = -25 2w = -25 Divide each side by '2'. w = -12.5 Simplifying w = -12.5Solution
w = {10, -12.5}
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