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Simplifying 0 = w2 + 4w + -192 Reorder the terms: 0 = -192 + 4w + w2 Solving 0 = -192 + 4w + w2 Solving for variable 'w'. Combine like terms: 0 + 192 = 192 192 + -4w + -1w2 = -192 + 4w + w2 + 192 + -4w + -1w2 Reorder the terms: 192 + -4w + -1w2 = -192 + 192 + 4w + -4w + w2 + -1w2 Combine like terms: -192 + 192 = 0 192 + -4w + -1w2 = 0 + 4w + -4w + w2 + -1w2 192 + -4w + -1w2 = 4w + -4w + w2 + -1w2 Combine like terms: 4w + -4w = 0 192 + -4w + -1w2 = 0 + w2 + -1w2 192 + -4w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 192 + -4w + -1w2 = 0 Factor a trinomial. (12 + -1w)(16 + w) = 0Subproblem 1
Set the factor '(12 + -1w)' equal to zero and attempt to solve: Simplifying 12 + -1w = 0 Solving 12 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1w = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1w = 0 + -12 -1w = 0 + -12 Combine like terms: 0 + -12 = -12 -1w = -12 Divide each side by '-1'. w = 12 Simplifying w = 12Subproblem 2
Set the factor '(16 + w)' equal to zero and attempt to solve: Simplifying 16 + w = 0 Solving 16 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + w = 0 + -16 Combine like terms: 16 + -16 = 0 0 + w = 0 + -16 w = 0 + -16 Combine like terms: 0 + -16 = -16 w = -16 Simplifying w = -16Solution
w = {12, -16}
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