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Simplifying 2w2 + -4w + 73 = w2 + -14w + 49 Reorder the terms: 73 + -4w + 2w2 = w2 + -14w + 49 Reorder the terms: 73 + -4w + 2w2 = 49 + -14w + w2 Solving 73 + -4w + 2w2 = 49 + -14w + w2 Solving for variable 'w'. Reorder the terms: 73 + -49 + -4w + 14w + 2w2 + -1w2 = 49 + -14w + w2 + -49 + 14w + -1w2 Combine like terms: 73 + -49 = 24 24 + -4w + 14w + 2w2 + -1w2 = 49 + -14w + w2 + -49 + 14w + -1w2 Combine like terms: -4w + 14w = 10w 24 + 10w + 2w2 + -1w2 = 49 + -14w + w2 + -49 + 14w + -1w2 Combine like terms: 2w2 + -1w2 = 1w2 24 + 10w + 1w2 = 49 + -14w + w2 + -49 + 14w + -1w2 Reorder the terms: 24 + 10w + 1w2 = 49 + -49 + -14w + 14w + w2 + -1w2 Combine like terms: 49 + -49 = 0 24 + 10w + 1w2 = 0 + -14w + 14w + w2 + -1w2 24 + 10w + 1w2 = -14w + 14w + w2 + -1w2 Combine like terms: -14w + 14w = 0 24 + 10w + 1w2 = 0 + w2 + -1w2 24 + 10w + 1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 24 + 10w + 1w2 = 0 Factor a trinomial. (6 + w)(4 + w) = 0Subproblem 1
Set the factor '(6 + w)' equal to zero and attempt to solve: Simplifying 6 + w = 0 Solving 6 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + w = 0 + -6 Combine like terms: 6 + -6 = 0 0 + w = 0 + -6 w = 0 + -6 Combine like terms: 0 + -6 = -6 w = -6 Simplifying w = -6Subproblem 2
Set the factor '(4 + w)' equal to zero and attempt to solve: Simplifying 4 + w = 0 Solving 4 + w = 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 + w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + w = 0 + -4 w = 0 + -4 Combine like terms: 0 + -4 = -4 w = -4 Simplifying w = -4Solution
w = {-6, -4}
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