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Simplifying 112 = -2w2 + 36w Reorder the terms: 112 = 36w + -2w2 Solving 112 = 36w + -2w2 Solving for variable 'w'. Reorder the terms: 112 + -36w + 2w2 = 36w + -36w + -2w2 + 2w2 Combine like terms: 36w + -36w = 0 112 + -36w + 2w2 = 0 + -2w2 + 2w2 112 + -36w + 2w2 = -2w2 + 2w2 Combine like terms: -2w2 + 2w2 = 0 112 + -36w + 2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(56 + -18w + w2) = 0 Factor a trinomial. 2((4 + -1w)(14 + -1w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -1w)' equal to zero and attempt to solve: Simplifying 4 + -1w = 0 Solving 4 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1w = 0 + -4 -1w = 0 + -4 Combine like terms: 0 + -4 = -4 -1w = -4 Divide each side by '-1'. w = 4 Simplifying w = 4Subproblem 2
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 = 14Solution
w = {4, 14}
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