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Simplifying -8(9q2 + -6q + 5) + 3(-1q2 + 4q + -3) = 0 Reorder the terms: -8(5 + -6q + 9q2) + 3(-1q2 + 4q + -3) = 0 (5 * -8 + -6q * -8 + 9q2 * -8) + 3(-1q2 + 4q + -3) = 0 (-40 + 48q + -72q2) + 3(-1q2 + 4q + -3) = 0 Reorder the terms: -40 + 48q + -72q2 + 3(-3 + 4q + -1q2) = 0 -40 + 48q + -72q2 + (-3 * 3 + 4q * 3 + -1q2 * 3) = 0 -40 + 48q + -72q2 + (-9 + 12q + -3q2) = 0 Reorder the terms: -40 + -9 + 48q + 12q + -72q2 + -3q2 = 0 Combine like terms: -40 + -9 = -49 -49 + 48q + 12q + -72q2 + -3q2 = 0 Combine like terms: 48q + 12q = 60q -49 + 60q + -72q2 + -3q2 = 0 Combine like terms: -72q2 + -3q2 = -75q2 -49 + 60q + -75q2 = 0 Solving -49 + 60q + -75q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by -75 the coefficient of the squared term: Divide each side by '-75'. 0.6533333333 + -0.8q + q2 = 0 Move the constant term to the right: Add '-0.6533333333' to each side of the equation. 0.6533333333 + -0.8q + -0.6533333333 + q2 = 0 + -0.6533333333 Reorder the terms: 0.6533333333 + -0.6533333333 + -0.8q + q2 = 0 + -0.6533333333 Combine like terms: 0.6533333333 + -0.6533333333 = 0.0000000000 0.0000000000 + -0.8q + q2 = 0 + -0.6533333333 -0.8q + q2 = 0 + -0.6533333333 Combine like terms: 0 + -0.6533333333 = -0.6533333333 -0.8q + q2 = -0.6533333333 The q term is -0.8q. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8q + 0.16 + q2 = -0.6533333333 + 0.16 Reorder the terms: 0.16 + -0.8q + q2 = -0.6533333333 + 0.16 Combine like terms: -0.6533333333 + 0.16 = -0.4933333333 0.16 + -0.8q + q2 = -0.4933333333 Factor a perfect square on the left side: (q + -0.4)(q + -0.4) = -0.4933333333 Can't calculate square root of the right side. The solution to this equation could not be determined.
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