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Simplifying 0 = 5w + w2 + -14 Reorder the terms: 0 = -14 + 5w + w2 Solving 0 = -14 + 5w + w2 Solving for variable 'w'. Combine like terms: 0 + 14 = 14 14 + -5w + -1w2 = -14 + 5w + w2 + 14 + -5w + -1w2 Reorder the terms: 14 + -5w + -1w2 = -14 + 14 + 5w + -5w + w2 + -1w2 Combine like terms: -14 + 14 = 0 14 + -5w + -1w2 = 0 + 5w + -5w + w2 + -1w2 14 + -5w + -1w2 = 5w + -5w + w2 + -1w2 Combine like terms: 5w + -5w = 0 14 + -5w + -1w2 = 0 + w2 + -1w2 14 + -5w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 14 + -5w + -1w2 = 0 Factor a trinomial. (2 + -1w)(7 + w) = 0Subproblem 1
Set the factor '(2 + -1w)' equal to zero and attempt to solve: Simplifying 2 + -1w = 0 Solving 2 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1w = 0 + -2 -1w = 0 + -2 Combine like terms: 0 + -2 = -2 -1w = -2 Divide each side by '-1'. w = 2 Simplifying w = 2Subproblem 2
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 = -7Solution
w = {2, -7}
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