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Simplifying 5w2 = 8w + -12 Reorder the terms: 5w2 = -12 + 8w Solving 5w2 = -12 + 8w Solving for variable 'w'. Reorder the terms: 12 + -8w + 5w2 = -12 + 8w + 12 + -8w Reorder the terms: 12 + -8w + 5w2 = -12 + 12 + 8w + -8w Combine like terms: -12 + 12 = 0 12 + -8w + 5w2 = 0 + 8w + -8w 12 + -8w + 5w2 = 8w + -8w Combine like terms: 8w + -8w = 0 12 + -8w + 5w2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.4 + -1.6w + w2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + -1.6w + -2.4 + w2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + -1.6w + w2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + -1.6w + w2 = 0 + -2.4 -1.6w + w2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 -1.6w + w2 = -2.4 The w term is -1.6w. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6w + 0.64 + w2 = -2.4 + 0.64 Reorder the terms: 0.64 + -1.6w + w2 = -2.4 + 0.64 Combine like terms: -2.4 + 0.64 = -1.76 0.64 + -1.6w + w2 = -1.76 Factor a perfect square on the left side: (w + -0.8)(w + -0.8) = -1.76 Can't calculate square root of the right side. The solution to this equation could not be determined.
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