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Simplifying w(2w + -2) = 40 Reorder the terms: w(-2 + 2w) = 40 (-2 * w + 2w * w) = 40 (-2w + 2w2) = 40 Solving -2w + 2w2 = 40 Solving for variable 'w'. Reorder the terms: -40 + -2w + 2w2 = 40 + -40 Combine like terms: 40 + -40 = 0 -40 + -2w + 2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-20 + -1w + w2) = 0 Factor a trinomial. 2((-4 + -1w)(5 + -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 '(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 = 5Solution
w = {-4, 5}
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