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