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Simplifying 100 = 3w2 + 13w Reorder the terms: 100 = 13w + 3w2 Solving 100 = 13w + 3w2 Solving for variable 'w'. Reorder the terms: 100 + -13w + -3w2 = 13w + -13w + 3w2 + -3w2 Combine like terms: 13w + -13w = 0 100 + -13w + -3w2 = 0 + 3w2 + -3w2 100 + -13w + -3w2 = 3w2 + -3w2 Combine like terms: 3w2 + -3w2 = 0 100 + -13w + -3w2 = 0 Factor a trinomial. (4 + -1w)(25 + 3w) = 0Subproblem 1
Set the factor '(4 + -1w)' equal to zero and attempt to solve: Simplifying 4 + -1w = 0 Solving 4 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1w = 0 + -4 -1w = 0 + -4 Combine like terms: 0 + -4 = -4 -1w = -4 Divide each side by '-1'. w = 4 Simplifying w = 4Subproblem 2
Set the factor '(25 + 3w)' equal to zero and attempt to solve: Simplifying 25 + 3w = 0 Solving 25 + 3w = 0 Move all terms containing w to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + 3w = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 3w = 0 + -25 3w = 0 + -25 Combine like terms: 0 + -25 = -25 3w = -25 Divide each side by '3'. w = -8.333333333 Simplifying w = -8.333333333Solution
w = {4, -8.333333333}
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