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Simplifying w(2w + 4) = 160 Reorder the terms: w(4 + 2w) = 160 (4 * w + 2w * w) = 160 (4w + 2w2) = 160 Solving 4w + 2w2 = 160 Solving for variable 'w'. Reorder the terms: -160 + 4w + 2w2 = 160 + -160 Combine like terms: 160 + -160 = 0 -160 + 4w + 2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-80 + 2w + w2) = 0 Factor a trinomial. 2((-10 + -1w)(8 + -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 '(8 + -1w)' equal to zero and attempt to solve: Simplifying 8 + -1w = 0 Solving 8 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1w = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1w = 0 + -8 -1w = 0 + -8 Combine like terms: 0 + -8 = -8 -1w = -8 Divide each side by '-1'. w = 8 Simplifying w = 8Solution
w = {-10, 8}
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