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Simplifying 5w2 = 25w + 120 Reorder the terms: 5w2 = 120 + 25w Solving 5w2 = 120 + 25w Solving for variable 'w'. Reorder the terms: -120 + -25w + 5w2 = 120 + 25w + -120 + -25w Reorder the terms: -120 + -25w + 5w2 = 120 + -120 + 25w + -25w Combine like terms: 120 + -120 = 0 -120 + -25w + 5w2 = 0 + 25w + -25w -120 + -25w + 5w2 = 25w + -25w Combine like terms: 25w + -25w = 0 -120 + -25w + 5w2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-24 + -5w + w2) = 0 Factor a trinomial. 5((-3 + -1w)(8 + -1w)) = 0 Ignore the factor 5.Subproblem 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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