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Simplifying 11 + q + -3q2 + 18q2 + -2 = 0 Reorder the terms: 11 + -2 + q + -3q2 + 18q2 = 0 Combine like terms: 11 + -2 = 9 9 + q + -3q2 + 18q2 = 0 Combine like terms: -3q2 + 18q2 = 15q2 9 + q + 15q2 = 0 Solving 9 + q + 15q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 0.6 + 0.06666666667q + q2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + 0.06666666667q + -0.6 + q2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + 0.06666666667q + q2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + 0.06666666667q + q2 = 0 + -0.6 0.06666666667q + q2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 0.06666666667q + q2 = -0.6 The q term is q. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.06666666667q + 0.25 + q2 = -0.6 + 0.25 Reorder the terms: 0.25 + 0.06666666667q + q2 = -0.6 + 0.25 Combine like terms: -0.6 + 0.25 = -0.35 0.25 + 0.06666666667q + q2 = -0.35 Factor a perfect square on the left side: (q + 0.5)(q + 0.5) = -0.35 Can't calculate square root of the right side. The solution to this equation could not be determined.
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