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Simplifying 2q2 + 3q + 5 = 0 Reorder the terms: 5 + 3q + 2q2 = 0 Solving 5 + 3q + 2q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + 1.5q + q2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 1.5q + -2.5 + q2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 1.5q + q2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 1.5q + q2 = 0 + -2.5 1.5q + q2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 1.5q + q2 = -2.5 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 = -2.5 + 0.5625 Reorder the terms: 0.5625 + 1.5q + q2 = -2.5 + 0.5625 Combine like terms: -2.5 + 0.5625 = -1.9375 0.5625 + 1.5q + q2 = -1.9375 Factor a perfect square on the left side: (q + 0.75)(q + 0.75) = -1.9375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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