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Simplifying 400 = 2w(50 + -2w) 400 = (50 * 2w + -2w * 2w) 400 = (100w + -4w2) Solving 400 = 100w + -4w2 Solving for variable 'w'. Reorder the terms: 400 + -100w + 4w2 = 100w + -100w + -4w2 + 4w2 Combine like terms: 100w + -100w = 0 400 + -100w + 4w2 = 0 + -4w2 + 4w2 400 + -100w + 4w2 = -4w2 + 4w2 Combine like terms: -4w2 + 4w2 = 0 400 + -100w + 4w2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(100 + -25w + w2) = 0 Factor a trinomial. 4((5 + -1w)(20 + -1w)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + -1w)' equal to zero and attempt to solve: Simplifying 5 + -1w = 0 Solving 5 + -1w = 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 + -1w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1w = 0 + -5 -1w = 0 + -5 Combine like terms: 0 + -5 = -5 -1w = -5 Divide each side by '-1'. w = 5 Simplifying w = 5Subproblem 2
Set the factor '(20 + -1w)' equal to zero and attempt to solve: Simplifying 20 + -1w = 0 Solving 20 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + -1w = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -1w = 0 + -20 -1w = 0 + -20 Combine like terms: 0 + -20 = -20 -1w = -20 Divide each side by '-1'. w = 20 Simplifying w = 20Solution
w = {5, 20}
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