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Simplifying 0 = 2w2 + -5w + 88 Reorder the terms: 0 = 88 + -5w + 2w2 Solving 0 = 88 + -5w + 2w2 Solving for variable 'w'. Combine like terms: 0 + -88 = -88 -88 + 5w + -2w2 = 88 + -5w + 2w2 + -88 + 5w + -2w2 Reorder the terms: -88 + 5w + -2w2 = 88 + -88 + -5w + 5w + 2w2 + -2w2 Combine like terms: 88 + -88 = 0 -88 + 5w + -2w2 = 0 + -5w + 5w + 2w2 + -2w2 -88 + 5w + -2w2 = -5w + 5w + 2w2 + -2w2 Combine like terms: -5w + 5w = 0 -88 + 5w + -2w2 = 0 + 2w2 + -2w2 -88 + 5w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 -88 + 5w + -2w2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 44 + -2.5w + w2 = 0 Move the constant term to the right: Add '-44' to each side of the equation. 44 + -2.5w + -44 + w2 = 0 + -44 Reorder the terms: 44 + -44 + -2.5w + w2 = 0 + -44 Combine like terms: 44 + -44 = 0 0 + -2.5w + w2 = 0 + -44 -2.5w + w2 = 0 + -44 Combine like terms: 0 + -44 = -44 -2.5w + w2 = -44 The w term is -2.5w. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5w + 1.5625 + w2 = -44 + 1.5625 Reorder the terms: 1.5625 + -2.5w + w2 = -44 + 1.5625 Combine like terms: -44 + 1.5625 = -42.4375 1.5625 + -2.5w + w2 = -42.4375 Factor a perfect square on the left side: (w + -1.25)(w + -1.25) = -42.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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