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Simplifying 638 = w2 + 7w Reorder the terms: 638 = 7w + w2 Solving 638 = 7w + w2 Solving for variable 'w'. Reorder the terms: 638 + -7w + -1w2 = 7w + -7w + w2 + -1w2 Combine like terms: 7w + -7w = 0 638 + -7w + -1w2 = 0 + w2 + -1w2 638 + -7w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 638 + -7w + -1w2 = 0 Factor a trinomial. (22 + -1w)(29 + w) = 0Subproblem 1
Set the factor '(22 + -1w)' equal to zero and attempt to solve: Simplifying 22 + -1w = 0 Solving 22 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + -1w = 0 + -22 Combine like terms: 22 + -22 = 0 0 + -1w = 0 + -22 -1w = 0 + -22 Combine like terms: 0 + -22 = -22 -1w = -22 Divide each side by '-1'. w = 22 Simplifying w = 22Subproblem 2
Set the factor '(29 + w)' equal to zero and attempt to solve: Simplifying 29 + w = 0 Solving 29 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-29' to each side of the equation. 29 + -29 + w = 0 + -29 Combine like terms: 29 + -29 = 0 0 + w = 0 + -29 w = 0 + -29 Combine like terms: 0 + -29 = -29 w = -29 Simplifying w = -29Solution
w = {22, -29}
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