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Simplifying 2q2 + 4q + -1 = 7q2 + -7q + 11 Reorder the terms: -1 + 4q + 2q2 = 7q2 + -7q + 11 Reorder the terms: -1 + 4q + 2q2 = 11 + -7q + 7q2 Solving -1 + 4q + 2q2 = 11 + -7q + 7q2 Solving for variable 'q'. Reorder the terms: -1 + -11 + 4q + 7q + 2q2 + -7q2 = 11 + -7q + 7q2 + -11 + 7q + -7q2 Combine like terms: -1 + -11 = -12 -12 + 4q + 7q + 2q2 + -7q2 = 11 + -7q + 7q2 + -11 + 7q + -7q2 Combine like terms: 4q + 7q = 11q -12 + 11q + 2q2 + -7q2 = 11 + -7q + 7q2 + -11 + 7q + -7q2 Combine like terms: 2q2 + -7q2 = -5q2 -12 + 11q + -5q2 = 11 + -7q + 7q2 + -11 + 7q + -7q2 Reorder the terms: -12 + 11q + -5q2 = 11 + -11 + -7q + 7q + 7q2 + -7q2 Combine like terms: 11 + -11 = 0 -12 + 11q + -5q2 = 0 + -7q + 7q + 7q2 + -7q2 -12 + 11q + -5q2 = -7q + 7q + 7q2 + -7q2 Combine like terms: -7q + 7q = 0 -12 + 11q + -5q2 = 0 + 7q2 + -7q2 -12 + 11q + -5q2 = 7q2 + -7q2 Combine like terms: 7q2 + -7q2 = 0 -12 + 11q + -5q2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 2.4 + -2.2q + q2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + -2.2q + -2.4 + q2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + -2.2q + q2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + -2.2q + q2 = 0 + -2.4 -2.2q + q2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 -2.2q + q2 = -2.4 The q term is -2.2q. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2q + 1.21 + q2 = -2.4 + 1.21 Reorder the terms: 1.21 + -2.2q + q2 = -2.4 + 1.21 Combine like terms: -2.4 + 1.21 = -1.19 1.21 + -2.2q + q2 = -1.19 Factor a perfect square on the left side: (q + -1.1)(q + -1.1) = -1.19 Can't calculate square root of the right side. The solution to this equation could not be determined.
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