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Simplifying 3(71 + -3q + 2q2) + q2 + 5q + -102 = 0 (71 * 3 + -3q * 3 + 2q2 * 3) + q2 + 5q + -102 = 0 (213 + -9q + 6q2) + q2 + 5q + -102 = 0 Reorder the terms: 213 + -102 + -9q + 5q + 6q2 + q2 = 0 Combine like terms: 213 + -102 = 111 111 + -9q + 5q + 6q2 + q2 = 0 Combine like terms: -9q + 5q = -4q 111 + -4q + 6q2 + q2 = 0 Combine like terms: 6q2 + q2 = 7q2 111 + -4q + 7q2 = 0 Solving 111 + -4q + 7q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 15.85714286 + -0.5714285714q + q2 = 0 Move the constant term to the right: Add '-15.85714286' to each side of the equation. 15.85714286 + -0.5714285714q + -15.85714286 + q2 = 0 + -15.85714286 Reorder the terms: 15.85714286 + -15.85714286 + -0.5714285714q + q2 = 0 + -15.85714286 Combine like terms: 15.85714286 + -15.85714286 = 0.00000000 0.00000000 + -0.5714285714q + q2 = 0 + -15.85714286 -0.5714285714q + q2 = 0 + -15.85714286 Combine like terms: 0 + -15.85714286 = -15.85714286 -0.5714285714q + q2 = -15.85714286 The q term is -0.5714285714q. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714q + 0.08163265305 + q2 = -15.85714286 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714q + q2 = -15.85714286 + 0.08163265305 Combine like terms: -15.85714286 + 0.08163265305 = -15.77551020695 0.08163265305 + -0.5714285714q + q2 = -15.77551020695 Factor a perfect square on the left side: (q + -0.2857142857)(q + -0.2857142857) = -15.77551020695 Can't calculate square root of the right side. The solution to this equation could not be determined.
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