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Simplifying 4w2 = 17w + -4 Reorder the terms: 4w2 = -4 + 17w Solving 4w2 = -4 + 17w Solving for variable 'w'. Reorder the terms: 4 + -17w + 4w2 = -4 + 17w + 4 + -17w Reorder the terms: 4 + -17w + 4w2 = -4 + 4 + 17w + -17w Combine like terms: -4 + 4 = 0 4 + -17w + 4w2 = 0 + 17w + -17w 4 + -17w + 4w2 = 17w + -17w Combine like terms: 17w + -17w = 0 4 + -17w + 4w2 = 0 Factor a trinomial. (1 + -4w)(4 + -1w) = 0Subproblem 1
Set the factor '(1 + -4w)' equal to zero and attempt to solve: Simplifying 1 + -4w = 0 Solving 1 + -4w = 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 + -4w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4w = 0 + -1 -4w = 0 + -1 Combine like terms: 0 + -1 = -1 -4w = -1 Divide each side by '-4'. w = 0.25 Simplifying w = 0.25Subproblem 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 = {0.25, 4}
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