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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((-10 + -1w)(7 + -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 '(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 = 7Solution
w = {-10, 7}
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