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Simplifying 2w2 = 3w + -8 Reorder the terms: 2w2 = -8 + 3w Solving 2w2 = -8 + 3w Solving for variable 'w'. Reorder the terms: 8 + -3w + 2w2 = -8 + 3w + 8 + -3w Reorder the terms: 8 + -3w + 2w2 = -8 + 8 + 3w + -3w Combine like terms: -8 + 8 = 0 8 + -3w + 2w2 = 0 + 3w + -3w 8 + -3w + 2w2 = 3w + -3w Combine like terms: 3w + -3w = 0 8 + -3w + 2w2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4 + -1.5w + w2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -1.5w + -4 + w2 = 0 + -4 Reorder the terms: 4 + -4 + -1.5w + w2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1.5w + w2 = 0 + -4 -1.5w + w2 = 0 + -4 Combine like terms: 0 + -4 = -4 -1.5w + w2 = -4 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 = -4 + 0.5625 Reorder the terms: 0.5625 + -1.5w + w2 = -4 + 0.5625 Combine like terms: -4 + 0.5625 = -3.4375 0.5625 + -1.5w + w2 = -3.4375 Factor a perfect square on the left side: (w + -0.75)(w + -0.75) = -3.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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