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Simplifying 2w2 + 3w + 35 = 0 Reorder the terms: 35 + 3w + 2w2 = 0 Solving 35 + 3w + 2w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 17.5 + 1.5w + w2 = 0 Move the constant term to the right: Add '-17.5' to each side of the equation. 17.5 + 1.5w + -17.5 + w2 = 0 + -17.5 Reorder the terms: 17.5 + -17.5 + 1.5w + w2 = 0 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + 1.5w + w2 = 0 + -17.5 1.5w + w2 = 0 + -17.5 Combine like terms: 0 + -17.5 = -17.5 1.5w + w2 = -17.5 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 = -17.5 + 0.5625 Reorder the terms: 0.5625 + 1.5w + w2 = -17.5 + 0.5625 Combine like terms: -17.5 + 0.5625 = -16.9375 0.5625 + 1.5w + w2 = -16.9375 Factor a perfect square on the left side: (w + 0.75)(w + 0.75) = -16.9375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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