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Simplifying 0 = -4w2 + 4w + 3 Reorder the terms: 0 = 3 + 4w + -4w2 Solving 0 = 3 + 4w + -4w2 Solving for variable 'w'. Combine like terms: 0 + -3 = -3 -3 + -4w + 4w2 = 3 + 4w + -4w2 + -3 + -4w + 4w2 Reorder the terms: -3 + -4w + 4w2 = 3 + -3 + 4w + -4w + -4w2 + 4w2 Combine like terms: 3 + -3 = 0 -3 + -4w + 4w2 = 0 + 4w + -4w + -4w2 + 4w2 -3 + -4w + 4w2 = 4w + -4w + -4w2 + 4w2 Combine like terms: 4w + -4w = 0 -3 + -4w + 4w2 = 0 + -4w2 + 4w2 -3 + -4w + 4w2 = -4w2 + 4w2 Combine like terms: -4w2 + 4w2 = 0 -3 + -4w + 4w2 = 0 Factor a trinomial. (-1 + -2w)(3 + -2w) = 0Subproblem 1
Set the factor '(-1 + -2w)' equal to zero and attempt to solve: Simplifying -1 + -2w = 0 Solving -1 + -2w = 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 + -2w = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2w = 0 + 1 -2w = 0 + 1 Combine like terms: 0 + 1 = 1 -2w = 1 Divide each side by '-2'. w = -0.5 Simplifying w = -0.5Subproblem 2
Set the factor '(3 + -2w)' equal to zero and attempt to solve: Simplifying 3 + -2w = 0 Solving 3 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2w = 0 + -3 -2w = 0 + -3 Combine like terms: 0 + -3 = -3 -2w = -3 Divide each side by '-2'. w = 1.5 Simplifying w = 1.5Solution
w = {-0.5, 1.5}
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