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Simplifying x = 0.64x2 + -7.68x + 31 Reorder the terms: x = 31 + -7.68x + 0.64x2 Solving x = 31 + -7.68x + 0.64x2 Solving for variable 'x'. Reorder the terms: -31 + x + 7.68x + -0.64x2 = 31 + -7.68x + 0.64x2 + -31 + 7.68x + -0.64x2 Combine like terms: x + 7.68x = 8.68x -31 + 8.68x + -0.64x2 = 31 + -7.68x + 0.64x2 + -31 + 7.68x + -0.64x2 Reorder the terms: -31 + 8.68x + -0.64x2 = 31 + -31 + -7.68x + 7.68x + 0.64x2 + -0.64x2 Combine like terms: 31 + -31 = 0 -31 + 8.68x + -0.64x2 = 0 + -7.68x + 7.68x + 0.64x2 + -0.64x2 -31 + 8.68x + -0.64x2 = -7.68x + 7.68x + 0.64x2 + -0.64x2 Combine like terms: -7.68x + 7.68x = 0.00 -31 + 8.68x + -0.64x2 = 0.00 + 0.64x2 + -0.64x2 -31 + 8.68x + -0.64x2 = 0.64x2 + -0.64x2 Combine like terms: 0.64x2 + -0.64x2 = 0.00 -31 + 8.68x + -0.64x2 = 0.00 Begin completing the square. Divide all terms by -0.64 the coefficient of the squared term: Divide each side by '-0.64'. 48.4375 + -13.5625x + x2 = 0 Move the constant term to the right: Add '-48.4375' to each side of the equation. 48.4375 + -13.5625x + -48.4375 + x2 = 0 + -48.4375 Reorder the terms: 48.4375 + -48.4375 + -13.5625x + x2 = 0 + -48.4375 Combine like terms: 48.4375 + -48.4375 = 0.0000 0.0000 + -13.5625x + x2 = 0 + -48.4375 -13.5625x + x2 = 0 + -48.4375 Combine like terms: 0 + -48.4375 = -48.4375 -13.5625x + x2 = -48.4375 The x term is -13.5625x. Take half its coefficient (-6.78125). Square it (45.98535156) and add it to both sides. Add '45.98535156' to each side of the equation. -13.5625x + 45.98535156 + x2 = -48.4375 + 45.98535156 Reorder the terms: 45.98535156 + -13.5625x + x2 = -48.4375 + 45.98535156 Combine like terms: -48.4375 + 45.98535156 = -2.45214844 45.98535156 + -13.5625x + x2 = -2.45214844 Factor a perfect square on the left side: (x + -6.78125)(x + -6.78125) = -2.45214844 Can't calculate square root of the right side. The solution to this equation could not be determined.
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