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Simplifying 6w2 + 3w + 5 = 0 Reorder the terms: 5 + 3w + 6w2 = 0 Solving 5 + 3w + 6w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.8333333333 + 0.5w + w2 = 0 Move the constant term to the right: Add '-0.8333333333' to each side of the equation. 0.8333333333 + 0.5w + -0.8333333333 + w2 = 0 + -0.8333333333 Reorder the terms: 0.8333333333 + -0.8333333333 + 0.5w + w2 = 0 + -0.8333333333 Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000 0.0000000000 + 0.5w + w2 = 0 + -0.8333333333 0.5w + w2 = 0 + -0.8333333333 Combine like terms: 0 + -0.8333333333 = -0.8333333333 0.5w + w2 = -0.8333333333 The w term is 0.5w. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5w + 0.0625 + w2 = -0.8333333333 + 0.0625 Reorder the terms: 0.0625 + 0.5w + w2 = -0.8333333333 + 0.0625 Combine like terms: -0.8333333333 + 0.0625 = -0.7708333333 0.0625 + 0.5w + w2 = -0.7708333333 Factor a perfect square on the left side: (w + 0.25)(w + 0.25) = -0.7708333333 Can't calculate square root of the right side. The solution to this equation could not be determined.
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