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Simplifying 1q + 2 = (-6q + -3)(8q + 4) Reorder the terms: 2 + 1q = (-6q + -3)(8q + 4) Reorder the terms: 2 + 1q = (-3 + -6q)(8q + 4) Reorder the terms: 2 + 1q = (-3 + -6q)(4 + 8q) Multiply (-3 + -6q) * (4 + 8q) 2 + 1q = (-3(4 + 8q) + -6q * (4 + 8q)) 2 + 1q = ((4 * -3 + 8q * -3) + -6q * (4 + 8q)) 2 + 1q = ((-12 + -24q) + -6q * (4 + 8q)) 2 + 1q = (-12 + -24q + (4 * -6q + 8q * -6q)) 2 + 1q = (-12 + -24q + (-24q + -48q2)) Combine like terms: -24q + -24q = -48q 2 + 1q = (-12 + -48q + -48q2) Solving 2 + 1q = -12 + -48q + -48q2 Solving for variable 'q'. Reorder the terms: 2 + 12 + 1q + 48q + 48q2 = -12 + -48q + -48q2 + 12 + 48q + 48q2 Combine like terms: 2 + 12 = 14 14 + 1q + 48q + 48q2 = -12 + -48q + -48q2 + 12 + 48q + 48q2 Combine like terms: 1q + 48q = 49q 14 + 49q + 48q2 = -12 + -48q + -48q2 + 12 + 48q + 48q2 Reorder the terms: 14 + 49q + 48q2 = -12 + 12 + -48q + 48q + -48q2 + 48q2 Combine like terms: -12 + 12 = 0 14 + 49q + 48q2 = 0 + -48q + 48q + -48q2 + 48q2 14 + 49q + 48q2 = -48q + 48q + -48q2 + 48q2 Combine like terms: -48q + 48q = 0 14 + 49q + 48q2 = 0 + -48q2 + 48q2 14 + 49q + 48q2 = -48q2 + 48q2 Combine like terms: -48q2 + 48q2 = 0 14 + 49q + 48q2 = 0 Begin completing the square. Divide all terms by 48 the coefficient of the squared term: Divide each side by '48'. 0.2916666667 + 1.020833333q + q2 = 0 Move the constant term to the right: Add '-0.2916666667' to each side of the equation. 0.2916666667 + 1.020833333q + -0.2916666667 + q2 = 0 + -0.2916666667 Reorder the terms: 0.2916666667 + -0.2916666667 + 1.020833333q + q2 = 0 + -0.2916666667 Combine like terms: 0.2916666667 + -0.2916666667 = 0.0000000000 0.0000000000 + 1.020833333q + q2 = 0 + -0.2916666667 1.020833333q + q2 = 0 + -0.2916666667 Combine like terms: 0 + -0.2916666667 = -0.2916666667 1.020833333q + q2 = -0.2916666667 The q term is 1.020833333q. Take half its coefficient (0.5104166665). Square it (0.2605251734) and add it to both sides. Add '0.2605251734' to each side of the equation. 1.020833333q + 0.2605251734 + q2 = -0.2916666667 + 0.2605251734 Reorder the terms: 0.2605251734 + 1.020833333q + q2 = -0.2916666667 + 0.2605251734 Combine like terms: -0.2916666667 + 0.2605251734 = -0.0311414933 0.2605251734 + 1.020833333q + q2 = -0.0311414933 Factor a perfect square on the left side: (q + 0.5104166665)(q + 0.5104166665) = -0.0311414933 Can't calculate square root of the right side. The solution to this equation could not be determined.
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