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Simplifying w(2w + -6) = 140 Reorder the terms: w(-6 + 2w) = 140 (-6 * w + 2w * w) = 140 (-6w + 2w2) = 140 Solving -6w + 2w2 = 140 Solving for variable 'w'. Reorder the terms: -140 + -6w + 2w2 = 140 + -140 Combine like terms: 140 + -140 = 0 -140 + -6w + 2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-70 + -3w + w2) = 0 Factor a trinomial. 2((-7 + -1w)(10 + -1w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -1w)' equal to zero and attempt to solve: Simplifying -7 + -1w = 0 Solving -7 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1w = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1w = 0 + 7 -1w = 0 + 7 Combine like terms: 0 + 7 = 7 -1w = 7 Divide each side by '-1'. w = -7 Simplifying w = -7Subproblem 2
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 = 10Solution
w = {-7, 10}
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