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Simplifying 5w2 = 19w + 4 Reorder the terms: 5w2 = 4 + 19w Solving 5w2 = 4 + 19w Solving for variable 'w'. Reorder the terms: -4 + -19w + 5w2 = 4 + 19w + -4 + -19w Reorder the terms: -4 + -19w + 5w2 = 4 + -4 + 19w + -19w Combine like terms: 4 + -4 = 0 -4 + -19w + 5w2 = 0 + 19w + -19w -4 + -19w + 5w2 = 19w + -19w Combine like terms: 19w + -19w = 0 -4 + -19w + 5w2 = 0 Factor a trinomial. (-1 + -5w)(4 + -1w) = 0Subproblem 1
Set the factor '(-1 + -5w)' equal to zero and attempt to solve: Simplifying -1 + -5w = 0 Solving -1 + -5w = 0 Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -5w = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5w = 0 + 1 -5w = 0 + 1 Combine like terms: 0 + 1 = 1 -5w = 1 Divide each side by '-5'. w = -0.2 Simplifying w = -0.2Subproblem 2
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 = 4Solution
w = {-0.2, 4}
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