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Simplifying (w + 5) * w = 84 Reorder the terms: (5 + w) * w = 84 Reorder the terms for easier multiplication: w(5 + w) = 84 (5 * w + w * w) = 84 (5w + w2) = 84 Solving 5w + w2 = 84 Solving for variable 'w'. Reorder the terms: -84 + 5w + w2 = 84 + -84 Combine like terms: 84 + -84 = 0 -84 + 5w + w2 = 0 Factor a trinomial. (-12 + -1w)(7 + -1w) = 0Subproblem 1
Set the factor '(-12 + -1w)' equal to zero and attempt to solve: Simplifying -12 + -1w = 0 Solving -12 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1w = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1w = 0 + 12 -1w = 0 + 12 Combine like terms: 0 + 12 = 12 -1w = 12 Divide each side by '-1'. w = -12 Simplifying w = -12Subproblem 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 = {-12, 7}
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