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Simplifying -54 = 2w2 + -3w Reorder the terms: -54 = -3w + 2w2 Solving -54 = -3w + 2w2 Solving for variable 'w'. Reorder the terms: -54 + 3w + -2w2 = -3w + 3w + 2w2 + -2w2 Combine like terms: -3w + 3w = 0 -54 + 3w + -2w2 = 0 + 2w2 + -2w2 -54 + 3w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 -54 + 3w + -2w2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 27 + -1.5w + w2 = 0 Move the constant term to the right: Add '-27' to each side of the equation. 27 + -1.5w + -27 + w2 = 0 + -27 Reorder the terms: 27 + -27 + -1.5w + w2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -1.5w + w2 = 0 + -27 -1.5w + w2 = 0 + -27 Combine like terms: 0 + -27 = -27 -1.5w + w2 = -27 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 = -27 + 0.5625 Reorder the terms: 0.5625 + -1.5w + w2 = -27 + 0.5625 Combine like terms: -27 + 0.5625 = -26.4375 0.5625 + -1.5w + w2 = -26.4375 Factor a perfect square on the left side: (w + -0.75)(w + -0.75) = -26.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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