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Simplifying 51w2 + -34w = 5797 Reorder the terms: -34w + 51w2 = 5797 Solving -34w + 51w2 = 5797 Solving for variable 'w'. Reorder the terms: -5797 + -34w + 51w2 = 5797 + -5797 Combine like terms: 5797 + -5797 = 0 -5797 + -34w + 51w2 = 0 Factor out the Greatest Common Factor (GCF), '17'. 17(-341 + -2w + 3w2) = 0 Factor a trinomial. 17((-31 + -3w)(11 + -1w)) = 0 Ignore the factor 17.Subproblem 1
Set the factor '(-31 + -3w)' equal to zero and attempt to solve: Simplifying -31 + -3w = 0 Solving -31 + -3w = 0 Move all terms containing w to the left, all other terms to the right. Add '31' to each side of the equation. -31 + 31 + -3w = 0 + 31 Combine like terms: -31 + 31 = 0 0 + -3w = 0 + 31 -3w = 0 + 31 Combine like terms: 0 + 31 = 31 -3w = 31 Divide each side by '-3'. w = -10.33333333 Simplifying w = -10.33333333Subproblem 2
Set the factor '(11 + -1w)' equal to zero and attempt to solve: Simplifying 11 + -1w = 0 Solving 11 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1w = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1w = 0 + -11 -1w = 0 + -11 Combine like terms: 0 + -11 = -11 -1w = -11 Divide each side by '-1'. w = 11 Simplifying w = 11Solution
w = {-10.33333333, 11}
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