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Simplifying (2w + 15)(2w + 14) = 420 Reorder the terms: (15 + 2w)(2w + 14) = 420 Reorder the terms: (15 + 2w)(14 + 2w) = 420 Multiply (15 + 2w) * (14 + 2w) (15(14 + 2w) + 2w * (14 + 2w)) = 420 ((14 * 15 + 2w * 15) + 2w * (14 + 2w)) = 420 ((210 + 30w) + 2w * (14 + 2w)) = 420 (210 + 30w + (14 * 2w + 2w * 2w)) = 420 (210 + 30w + (28w + 4w2)) = 420 Combine like terms: 30w + 28w = 58w (210 + 58w + 4w2) = 420 Solving 210 + 58w + 4w2 = 420 Solving for variable 'w'. Reorder the terms: 210 + -420 + 58w + 4w2 = 420 + -420 Combine like terms: 210 + -420 = -210 -210 + 58w + 4w2 = 420 + -420 Combine like terms: 420 + -420 = 0 -210 + 58w + 4w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-105 + 29w + 2w2) = 0 Factor a trinomial. 2((-35 + -2w)(3 + -1w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-35 + -2w)' equal to zero and attempt to solve: Simplifying -35 + -2w = 0 Solving -35 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + -2w = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -2w = 0 + 35 -2w = 0 + 35 Combine like terms: 0 + 35 = 35 -2w = 35 Divide each side by '-2'. w = -17.5 Simplifying w = -17.5Subproblem 2
Set the factor '(3 + -1w)' equal to zero and attempt to solve: Simplifying 3 + -1w = 0 Solving 3 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1w = 0 + -3 -1w = 0 + -3 Combine like terms: 0 + -3 = -3 -1w = -3 Divide each side by '-1'. w = 3 Simplifying w = 3Solution
w = {-17.5, 3}
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