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Simplifying -6(4q2 + -4q + 5) + 5(-1q2 + 6q + -3) = 0 Reorder the terms: -6(5 + -4q + 4q2) + 5(-1q2 + 6q + -3) = 0 (5 * -6 + -4q * -6 + 4q2 * -6) + 5(-1q2 + 6q + -3) = 0 (-30 + 24q + -24q2) + 5(-1q2 + 6q + -3) = 0 Reorder the terms: -30 + 24q + -24q2 + 5(-3 + 6q + -1q2) = 0 -30 + 24q + -24q2 + (-3 * 5 + 6q * 5 + -1q2 * 5) = 0 -30 + 24q + -24q2 + (-15 + 30q + -5q2) = 0 Reorder the terms: -30 + -15 + 24q + 30q + -24q2 + -5q2 = 0 Combine like terms: -30 + -15 = -45 -45 + 24q + 30q + -24q2 + -5q2 = 0 Combine like terms: 24q + 30q = 54q -45 + 54q + -24q2 + -5q2 = 0 Combine like terms: -24q2 + -5q2 = -29q2 -45 + 54q + -29q2 = 0 Solving -45 + 54q + -29q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by -29 the coefficient of the squared term: Divide each side by '-29'. 1.551724138 + -1.862068966q + q2 = 0 Move the constant term to the right: Add '-1.551724138' to each side of the equation. 1.551724138 + -1.862068966q + -1.551724138 + q2 = 0 + -1.551724138 Reorder the terms: 1.551724138 + -1.551724138 + -1.862068966q + q2 = 0 + -1.551724138 Combine like terms: 1.551724138 + -1.551724138 = 0.000000000 0.000000000 + -1.862068966q + q2 = 0 + -1.551724138 -1.862068966q + q2 = 0 + -1.551724138 Combine like terms: 0 + -1.551724138 = -1.551724138 -1.862068966q + q2 = -1.551724138 The q term is -1.862068966q. Take half its coefficient (-0.931034483). Square it (0.8668252085) and add it to both sides. Add '0.8668252085' to each side of the equation. -1.862068966q + 0.8668252085 + q2 = -1.551724138 + 0.8668252085 Reorder the terms: 0.8668252085 + -1.862068966q + q2 = -1.551724138 + 0.8668252085 Combine like terms: -1.551724138 + 0.8668252085 = -0.6848989295 0.8668252085 + -1.862068966q + q2 = -0.6848989295 Factor a perfect square on the left side: (q + -0.931034483)(q + -0.931034483) = -0.6848989295 Can't calculate square root of the right side. The solution to this equation could not be determined.
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