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Simplifying 32 + 4c(c + -1) = (4c + 5c) Reorder the terms: 32 + 4c(-1 + c) = (4c + 5c) 32 + (-1 * 4c + c * 4c) = (4c + 5c) 32 + (-4c + 4c2) = (4c + 5c) Combine like terms: 4c + 5c = 9c 32 + -4c + 4c2 = (9c) 32 + -4c + 4c2 = (9c) Solving 32 + -4c + 4c2 = (9c) Solving for variable 'c'. Reorder the terms: 32 + -4c + (-9c) + 4c2 = (9c) + (-9c) Combine like terms: -4c + (-9c) = -13c 32 + -13c + 4c2 = (9c) + (-9c) Combine like terms: (9c) + (-9c) = 0 32 + -13c + 4c2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 8 + -3.25c + c2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -3.25c + -8 + c2 = 0 + -8 Reorder the terms: 8 + -8 + -3.25c + c2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3.25c + c2 = 0 + -8 -3.25c + c2 = 0 + -8 Combine like terms: 0 + -8 = -8 -3.25c + c2 = -8 The c term is -3.25c. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25c + 2.640625 + c2 = -8 + 2.640625 Reorder the terms: 2.640625 + -3.25c + c2 = -8 + 2.640625 Combine like terms: -8 + 2.640625 = -5.359375 2.640625 + -3.25c + c2 = -5.359375 Factor a perfect square on the left side: (c + -1.625)(c + -1.625) = -5.359375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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