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Simplifying w2 = 5w + 24 Reorder the terms: w2 = 24 + 5w Solving w2 = 24 + 5w Solving for variable 'w'. Reorder the terms: -24 + -5w + w2 = 24 + 5w + -24 + -5w Reorder the terms: -24 + -5w + w2 = 24 + -24 + 5w + -5w Combine like terms: 24 + -24 = 0 -24 + -5w + w2 = 0 + 5w + -5w -24 + -5w + w2 = 5w + -5w Combine like terms: 5w + -5w = 0 -24 + -5w + w2 = 0 Factor a trinomial. (-3 + -1w)(8 + -1w) = 0Subproblem 1
Set the factor '(-3 + -1w)' equal to zero and attempt to solve: Simplifying -3 + -1w = 0 Solving -3 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1w = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1w = 0 + 3 -1w = 0 + 3 Combine like terms: 0 + 3 = 3 -1w = 3 Divide each side by '-1'. w = -3 Simplifying w = -3Subproblem 2
Set the factor '(8 + -1w)' equal to zero and attempt to solve: Simplifying 8 + -1w = 0 Solving 8 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1w = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1w = 0 + -8 -1w = 0 + -8 Combine like terms: 0 + -8 = -8 -1w = -8 Divide each side by '-1'. w = 8 Simplifying w = 8Solution
w = {-3, 8}
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