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Simplifying 2q2 + 3q = -6 Reorder the terms: 3q + 2q2 = -6 Solving 3q + 2q2 = -6 Solving for variable 'q'. Reorder the terms: 6 + 3q + 2q2 = -6 + 6 Combine like terms: -6 + 6 = 0 6 + 3q + 2q2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3 + 1.5q + q2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 1.5q + -3 + q2 = 0 + -3 Reorder the terms: 3 + -3 + 1.5q + q2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 1.5q + q2 = 0 + -3 1.5q + q2 = 0 + -3 Combine like terms: 0 + -3 = -3 1.5q + q2 = -3 The q term is 1.5q. 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. 1.5q + 0.5625 + q2 = -3 + 0.5625 Reorder the terms: 0.5625 + 1.5q + q2 = -3 + 0.5625 Combine like terms: -3 + 0.5625 = -2.4375 0.5625 + 1.5q + q2 = -2.4375 Factor a perfect square on the left side: (q + 0.75)(q + 0.75) = -2.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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