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Simplifying 2w2 + -19w + 53 = w2 + -14w + 49 Reorder the terms: 53 + -19w + 2w2 = w2 + -14w + 49 Reorder the terms: 53 + -19w + 2w2 = 49 + -14w + w2 Solving 53 + -19w + 2w2 = 49 + -14w + w2 Solving for variable 'w'. Reorder the terms: 53 + -49 + -19w + 14w + 2w2 + -1w2 = 49 + -14w + w2 + -49 + 14w + -1w2 Combine like terms: 53 + -49 = 4 4 + -19w + 14w + 2w2 + -1w2 = 49 + -14w + w2 + -49 + 14w + -1w2 Combine like terms: -19w + 14w = -5w 4 + -5w + 2w2 + -1w2 = 49 + -14w + w2 + -49 + 14w + -1w2 Combine like terms: 2w2 + -1w2 = 1w2 4 + -5w + 1w2 = 49 + -14w + w2 + -49 + 14w + -1w2 Reorder the terms: 4 + -5w + 1w2 = 49 + -49 + -14w + 14w + w2 + -1w2 Combine like terms: 49 + -49 = 0 4 + -5w + 1w2 = 0 + -14w + 14w + w2 + -1w2 4 + -5w + 1w2 = -14w + 14w + w2 + -1w2 Combine like terms: -14w + 14w = 0 4 + -5w + 1w2 = 0 + w2 + -1w2 4 + -5w + 1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 4 + -5w + 1w2 = 0 Factor a trinomial. (1 + -1w)(4 + -1w) = 0Subproblem 1
Set the factor '(1 + -1w)' equal to zero and attempt to solve: Simplifying 1 + -1w = 0 Solving 1 + -1w = 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 + -1w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1w = 0 + -1 -1w = 0 + -1 Combine like terms: 0 + -1 = -1 -1w = -1 Divide each side by '-1'. w = 1 Simplifying w = 1Subproblem 2
Set the factor '(4 + -1w)' equal to zero and attempt to solve: Simplifying 4 + -1w = 0 Solving 4 + -1w = 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 + -1w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1w = 0 + -4 -1w = 0 + -4 Combine like terms: 0 + -4 = -4 -1w = -4 Divide each side by '-1'. w = 4 Simplifying w = 4Solution
w = {1, 4}
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