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Simplifying 0 = 4w2 + -19w + 15 Reorder the terms: 0 = 15 + -19w + 4w2 Solving 0 = 15 + -19w + 4w2 Solving for variable 'w'. Combine like terms: 0 + -15 = -15 -15 + 19w + -4w2 = 15 + -19w + 4w2 + -15 + 19w + -4w2 Reorder the terms: -15 + 19w + -4w2 = 15 + -15 + -19w + 19w + 4w2 + -4w2 Combine like terms: 15 + -15 = 0 -15 + 19w + -4w2 = 0 + -19w + 19w + 4w2 + -4w2 -15 + 19w + -4w2 = -19w + 19w + 4w2 + -4w2 Combine like terms: -19w + 19w = 0 -15 + 19w + -4w2 = 0 + 4w2 + -4w2 -15 + 19w + -4w2 = 4w2 + -4w2 Combine like terms: 4w2 + -4w2 = 0 -15 + 19w + -4w2 = 0 Factor a trinomial. (-15 + 4w)(1 + -1w) = 0Subproblem 1
Set the factor '(-15 + 4w)' equal to zero and attempt to solve: Simplifying -15 + 4w = 0 Solving -15 + 4w = 0 Move all terms containing w to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + 4w = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 4w = 0 + 15 4w = 0 + 15 Combine like terms: 0 + 15 = 15 4w = 15 Divide each side by '4'. w = 3.75 Simplifying w = 3.75Subproblem 2
Set the factor '(1 + -1w)' equal to zero and attempt to solve: Simplifying 1 + -1w = 0 Solving 1 + -1w = 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 + -1w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1w = 0 + -1 -1w = 0 + -1 Combine like terms: 0 + -1 = -1 -1w = -1 Divide each side by '-1'. w = 1 Simplifying w = 1Solution
w = {3.75, 1}
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