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Simplifying (10 + w) * w = 264 Reorder the terms for easier multiplication: w(10 + w) = 264 (10 * w + w * w) = 264 (10w + w2) = 264 Solving 10w + w2 = 264 Solving for variable 'w'. Reorder the terms: -264 + 10w + w2 = 264 + -264 Combine like terms: 264 + -264 = 0 -264 + 10w + w2 = 0 Factor a trinomial. (-22 + -1w)(12 + -1w) = 0Subproblem 1
Set the factor '(-22 + -1w)' equal to zero and attempt to solve: Simplifying -22 + -1w = 0 Solving -22 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + -1w = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -1w = 0 + 22 -1w = 0 + 22 Combine like terms: 0 + 22 = 22 -1w = 22 Divide each side by '-1'. w = -22 Simplifying w = -22Subproblem 2
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 = 12Solution
w = {-22, 12}
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