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Simplifying 84 = (2w + 2) * w Reorder the terms: 84 = (2 + 2w) * w Reorder the terms for easier multiplication: 84 = w(2 + 2w) 84 = (2 * w + 2w * w) 84 = (2w + 2w2) Solving 84 = 2w + 2w2 Solving for variable 'w'. Reorder the terms: 84 + -2w + -2w2 = 2w + -2w + 2w2 + -2w2 Combine like terms: 2w + -2w = 0 84 + -2w + -2w2 = 0 + 2w2 + -2w2 84 + -2w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 84 + -2w + -2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(42 + -1w + -1w2) = 0 Factor a trinomial. 2((6 + -1w)(7 + w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + -1w)' equal to zero and attempt to solve: Simplifying 6 + -1w = 0 Solving 6 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1w = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1w = 0 + -6 -1w = 0 + -6 Combine like terms: 0 + -6 = -6 -1w = -6 Divide each side by '-1'. w = 6 Simplifying w = 6Subproblem 2
Set the factor '(7 + w)' equal to zero and attempt to solve: Simplifying 7 + w = 0 Solving 7 + w = 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 + w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + w = 0 + -7 w = 0 + -7 Combine like terms: 0 + -7 = -7 w = -7 Simplifying w = -7Solution
w = {6, -7}
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