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Simplifying 10w = w2 + 21 Reorder the terms: 10w = 21 + w2 Solving 10w = 21 + w2 Solving for variable 'w'. Reorder the terms: -21 + 10w + -1w2 = 21 + w2 + -21 + -1w2 Reorder the terms: -21 + 10w + -1w2 = 21 + -21 + w2 + -1w2 Combine like terms: 21 + -21 = 0 -21 + 10w + -1w2 = 0 + w2 + -1w2 -21 + 10w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 -21 + 10w + -1w2 = 0 Factor a trinomial. (-7 + w)(3 + -1w) = 0Subproblem 1
Set the factor '(-7 + w)' equal to zero and attempt to solve: Simplifying -7 + w = 0 Solving -7 + w = 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 + w = 0 + 7 Combine like terms: -7 + 7 = 0 0 + w = 0 + 7 w = 0 + 7 Combine like terms: 0 + 7 = 7 w = 7 Simplifying w = 7Subproblem 2
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 = 3Solution
w = {7, 3}
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