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Simplifying 10w2 = 9w + -15 Reorder the terms: 10w2 = -15 + 9w Solving 10w2 = -15 + 9w Solving for variable 'w'. Reorder the terms: 15 + -9w + 10w2 = -15 + 9w + 15 + -9w Reorder the terms: 15 + -9w + 10w2 = -15 + 15 + 9w + -9w Combine like terms: -15 + 15 = 0 15 + -9w + 10w2 = 0 + 9w + -9w 15 + -9w + 10w2 = 9w + -9w Combine like terms: 9w + -9w = 0 15 + -9w + 10w2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 1.5 + -0.9w + w2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -0.9w + -1.5 + w2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -0.9w + w2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -0.9w + w2 = 0 + -1.5 -0.9w + w2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -0.9w + w2 = -1.5 The w term is -0.9w. Take half its coefficient (-0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. -0.9w + 0.2025 + w2 = -1.5 + 0.2025 Reorder the terms: 0.2025 + -0.9w + w2 = -1.5 + 0.2025 Combine like terms: -1.5 + 0.2025 = -1.2975 0.2025 + -0.9w + w2 = -1.2975 Factor a perfect square on the left side: (w + -0.45)(w + -0.45) = -1.2975 Can't calculate square root of the right side. The solution to this equation could not be determined.
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