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Simplifying 14 = w(3 + -2w) 14 = (3 * w + -2w * w) 14 = (3w + -2w2) Solving 14 = 3w + -2w2 Solving for variable 'w'. Reorder the terms: 14 + -3w + 2w2 = 3w + -3w + -2w2 + 2w2 Combine like terms: 3w + -3w = 0 14 + -3w + 2w2 = 0 + -2w2 + 2w2 14 + -3w + 2w2 = -2w2 + 2w2 Combine like terms: -2w2 + 2w2 = 0 14 + -3w + 2w2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7 + -1.5w + w2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -1.5w + -7 + w2 = 0 + -7 Reorder the terms: 7 + -7 + -1.5w + w2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1.5w + w2 = 0 + -7 -1.5w + w2 = 0 + -7 Combine like terms: 0 + -7 = -7 -1.5w + w2 = -7 The w term is -1.5w. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5w + 0.5625 + w2 = -7 + 0.5625 Reorder the terms: 0.5625 + -1.5w + w2 = -7 + 0.5625 Combine like terms: -7 + 0.5625 = -6.4375 0.5625 + -1.5w + w2 = -6.4375 Factor a perfect square on the left side: (w + -0.75)(w + -0.75) = -6.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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