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Simplifying w(2w + -2) = 220 Reorder the terms: w(-2 + 2w) = 220 (-2 * w + 2w * w) = 220 (-2w + 2w2) = 220 Solving -2w + 2w2 = 220 Solving for variable 'w'. Reorder the terms: -220 + -2w + 2w2 = 220 + -220 Combine like terms: 220 + -220 = 0 -220 + -2w + 2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-110 + -1w + w2) = 0 Factor a trinomial. 2((-10 + -1w)(11 + -1w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + -1w)' equal to zero and attempt to solve: Simplifying -10 + -1w = 0 Solving -10 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -1w = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1w = 0 + 10 -1w = 0 + 10 Combine like terms: 0 + 10 = 10 -1w = 10 Divide each side by '-1'. w = -10 Simplifying w = -10Subproblem 2
Set the factor '(11 + -1w)' equal to zero and attempt to solve: Simplifying 11 + -1w = 0 Solving 11 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1w = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1w = 0 + -11 -1w = 0 + -11 Combine like terms: 0 + -11 = -11 -1w = -11 Divide each side by '-1'. w = 11 Simplifying w = 11Solution
w = {-10, 11}
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