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Simplifying 2w2 + -18w + 28 + -1w2 + 14w + -49 = 0 Reorder the terms: 28 + -49 + -18w + 14w + 2w2 + -1w2 = 0 Combine like terms: 28 + -49 = -21 -21 + -18w + 14w + 2w2 + -1w2 = 0 Combine like terms: -18w + 14w = -4w -21 + -4w + 2w2 + -1w2 = 0 Combine like terms: 2w2 + -1w2 = 1w2 -21 + -4w + 1w2 = 0 Solving -21 + -4w + 1w2 = 0 Solving for variable 'w'. Factor a trinomial. (-3 + -1w)(7 + -1w) = 0Subproblem 1
Set the factor '(-3 + -1w)' equal to zero and attempt to solve: Simplifying -3 + -1w = 0 Solving -3 + -1w = 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 + -1w = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1w = 0 + 3 -1w = 0 + 3 Combine like terms: 0 + 3 = 3 -1w = 3 Divide each side by '-1'. w = -3 Simplifying w = -3Subproblem 2
Set the factor '(7 + -1w)' equal to zero and attempt to solve: Simplifying 7 + -1w = 0 Solving 7 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1w = 0 + -7 -1w = 0 + -7 Combine like terms: 0 + -7 = -7 -1w = -7 Divide each side by '-1'. w = 7 Simplifying w = 7Solution
w = {-3, 7}
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