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Simplifying 224 = (12 + 2w)(w) Reorder the terms for easier multiplication: 224 = w(12 + 2w) 224 = (12 * w + 2w * w) 224 = (12w + 2w2) Solving 224 = 12w + 2w2 Solving for variable 'w'. Reorder the terms: 224 + -12w + -2w2 = 12w + -12w + 2w2 + -2w2 Combine like terms: 12w + -12w = 0 224 + -12w + -2w2 = 0 + 2w2 + -2w2 224 + -12w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 224 + -12w + -2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(112 + -6w + -1w2) = 0 Factor a trinomial. 2((8 + -1w)(14 + w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + -1w)' equal to zero and attempt to solve: Simplifying 8 + -1w = 0 Solving 8 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1w = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1w = 0 + -8 -1w = 0 + -8 Combine like terms: 0 + -8 = -8 -1w = -8 Divide each side by '-1'. w = 8 Simplifying w = 8Subproblem 2
Set the factor '(14 + w)' equal to zero and attempt to solve: Simplifying 14 + w = 0 Solving 14 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + w = 0 + -14 Combine like terms: 14 + -14 = 0 0 + w = 0 + -14 w = 0 + -14 Combine like terms: 0 + -14 = -14 w = -14 Simplifying w = -14Solution
w = {8, -14}
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