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Simplifying (4w2) + -19w + -30 = 6 + -2w2 Reorder the terms: -30 + -19w + (4w2) = 6 + -2w2 Solving -30 + -19w + (4w2) = 6 + -2w2 Solving for variable 'w'. Reorder the terms: -30 + -6 + -19w + (4w2) + 2w2 = 6 + -2w2 + -6 + 2w2 Combine like terms: -30 + -6 = -36 -36 + -19w + (4w2) + 2w2 = 6 + -2w2 + -6 + 2w2 Combine like terms: (4w2) + 2w2 = 6w2 -36 + -19w + 6w2 = 6 + -2w2 + -6 + 2w2 Reorder the terms: -36 + -19w + 6w2 = 6 + -6 + -2w2 + 2w2 Combine like terms: 6 + -6 = 0 -36 + -19w + 6w2 = 0 + -2w2 + 2w2 -36 + -19w + 6w2 = -2w2 + 2w2 Combine like terms: -2w2 + 2w2 = 0 -36 + -19w + 6w2 = 0 Factor a trinomial. (-4 + -3w)(9 + -2w) = 0Subproblem 1
Set the factor '(-4 + -3w)' equal to zero and attempt to solve: Simplifying -4 + -3w = 0 Solving -4 + -3w = 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 + -3w = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3w = 0 + 4 -3w = 0 + 4 Combine like terms: 0 + 4 = 4 -3w = 4 Divide each side by '-3'. w = -1.333333333 Simplifying w = -1.333333333Subproblem 2
Set the factor '(9 + -2w)' equal to zero and attempt to solve: Simplifying 9 + -2w = 0 Solving 9 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2w = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2w = 0 + -9 -2w = 0 + -9 Combine like terms: 0 + -9 = -9 -2w = -9 Divide each side by '-2'. w = 4.5 Simplifying w = 4.5Solution
w = {-1.333333333, 4.5}
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