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Simplifying (7 + w)(w) = 144 Reorder the terms for easier multiplication: w(7 + w) = 144 (7 * w + w * w) = 144 (7w + w2) = 144 Solving 7w + w2 = 144 Solving for variable 'w'. Reorder the terms: -144 + 7w + w2 = 144 + -144 Combine like terms: 144 + -144 = 0 -144 + 7w + w2 = 0 Factor a trinomial. (-16 + -1w)(9 + -1w) = 0Subproblem 1
Set the factor '(-16 + -1w)' equal to zero and attempt to solve: Simplifying -16 + -1w = 0 Solving -16 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + -1w = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -1w = 0 + 16 -1w = 0 + 16 Combine like terms: 0 + 16 = 16 -1w = 16 Divide each side by '-1'. w = -16 Simplifying w = -16Subproblem 2
Set the factor '(9 + -1w)' equal to zero and attempt to solve: Simplifying 9 + -1w = 0 Solving 9 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1w = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1w = 0 + -9 -1w = 0 + -9 Combine like terms: 0 + -9 = -9 -1w = -9 Divide each side by '-1'. w = 9 Simplifying w = 9Solution
w = {-16, 9}
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