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Simplifying 2w2 = 7w + -7 Reorder the terms: 2w2 = -7 + 7w Solving 2w2 = -7 + 7w Solving for variable 'w'. Reorder the terms: 7 + -7w + 2w2 = -7 + 7w + 7 + -7w Reorder the terms: 7 + -7w + 2w2 = -7 + 7 + 7w + -7w Combine like terms: -7 + 7 = 0 7 + -7w + 2w2 = 0 + 7w + -7w 7 + -7w + 2w2 = 7w + -7w Combine like terms: 7w + -7w = 0 7 + -7w + 2w2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.5 + -3.5w + w2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -3.5w + -3.5 + w2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -3.5w + w2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -3.5w + w2 = 0 + -3.5 -3.5w + w2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -3.5w + w2 = -3.5 The w term is -3.5w. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5w + 3.0625 + w2 = -3.5 + 3.0625 Reorder the terms: 3.0625 + -3.5w + w2 = -3.5 + 3.0625 Combine like terms: -3.5 + 3.0625 = -0.4375 3.0625 + -3.5w + w2 = -0.4375 Factor a perfect square on the left side: (w + -1.75)(w + -1.75) = -0.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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