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Simplifying 4w2 = 19w + 5 Reorder the terms: 4w2 = 5 + 19w Solving 4w2 = 5 + 19w Solving for variable 'w'. Reorder the terms: -5 + -19w + 4w2 = 5 + 19w + -5 + -19w Reorder the terms: -5 + -19w + 4w2 = 5 + -5 + 19w + -19w Combine like terms: 5 + -5 = 0 -5 + -19w + 4w2 = 0 + 19w + -19w -5 + -19w + 4w2 = 19w + -19w Combine like terms: 19w + -19w = 0 -5 + -19w + 4w2 = 0 Factor a trinomial. (-1 + -4w)(5 + -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 '(5 + -1w)' equal to zero and attempt to solve: Simplifying 5 + -1w = 0 Solving 5 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1w = 0 + -5 -1w = 0 + -5 Combine like terms: 0 + -5 = -5 -1w = -5 Divide each side by '-1'. w = 5 Simplifying w = 5Solution
w = {-0.25, 5}
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