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Simplifying (52 + w)(w) = 8160 Reorder the terms for easier multiplication: w(52 + w) = 8160 (52 * w + w * w) = 8160 (52w + w2) = 8160 Solving 52w + w2 = 8160 Solving for variable 'w'. Reorder the terms: -8160 + 52w + w2 = 8160 + -8160 Combine like terms: 8160 + -8160 = 0 -8160 + 52w + w2 = 0 Factor a trinomial. (-120 + -1w)(68 + -1w) = 0Subproblem 1
Set the factor '(-120 + -1w)' equal to zero and attempt to solve: Simplifying -120 + -1w = 0 Solving -120 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '120' to each side of the equation. -120 + 120 + -1w = 0 + 120 Combine like terms: -120 + 120 = 0 0 + -1w = 0 + 120 -1w = 0 + 120 Combine like terms: 0 + 120 = 120 -1w = 120 Divide each side by '-1'. w = -120 Simplifying w = -120Subproblem 2
Set the factor '(68 + -1w)' equal to zero and attempt to solve: Simplifying 68 + -1w = 0 Solving 68 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-68' to each side of the equation. 68 + -68 + -1w = 0 + -68 Combine like terms: 68 + -68 = 0 0 + -1w = 0 + -68 -1w = 0 + -68 Combine like terms: 0 + -68 = -68 -1w = -68 Divide each side by '-1'. w = 68 Simplifying w = 68Solution
w = {-120, 68}
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