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Simplifying w2 + -14w + 49 = 2w2 + -23w + 69 Reorder the terms: 49 + -14w + w2 = 2w2 + -23w + 69 Reorder the terms: 49 + -14w + w2 = 69 + -23w + 2w2 Solving 49 + -14w + w2 = 69 + -23w + 2w2 Solving for variable 'w'. Reorder the terms: 49 + -69 + -14w + 23w + w2 + -2w2 = 69 + -23w + 2w2 + -69 + 23w + -2w2 Combine like terms: 49 + -69 = -20 -20 + -14w + 23w + w2 + -2w2 = 69 + -23w + 2w2 + -69 + 23w + -2w2 Combine like terms: -14w + 23w = 9w -20 + 9w + w2 + -2w2 = 69 + -23w + 2w2 + -69 + 23w + -2w2 Combine like terms: w2 + -2w2 = -1w2 -20 + 9w + -1w2 = 69 + -23w + 2w2 + -69 + 23w + -2w2 Reorder the terms: -20 + 9w + -1w2 = 69 + -69 + -23w + 23w + 2w2 + -2w2 Combine like terms: 69 + -69 = 0 -20 + 9w + -1w2 = 0 + -23w + 23w + 2w2 + -2w2 -20 + 9w + -1w2 = -23w + 23w + 2w2 + -2w2 Combine like terms: -23w + 23w = 0 -20 + 9w + -1w2 = 0 + 2w2 + -2w2 -20 + 9w + -1w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 -20 + 9w + -1w2 = 0 Factor a trinomial. (-5 + w)(4 + -1w) = 0Subproblem 1
Set the factor '(-5 + w)' equal to zero and attempt to solve: Simplifying -5 + w = 0 Solving -5 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + w = 0 + 5 Combine like terms: -5 + 5 = 0 0 + w = 0 + 5 w = 0 + 5 Combine like terms: 0 + 5 = 5 w = 5 Simplifying w = 5Subproblem 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 = {5, 4}
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