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Simplifying 24q + 3456 = -2q2 Reorder the terms: 3456 + 24q = -2q2 Solving 3456 + 24q = -2q2 Solving for variable 'q'. Combine like terms: -2q2 + 2q2 = 0 3456 + 24q + 2q2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1728 + 12q + q2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1728 + 12q + q2)' equal to zero and attempt to solve: Simplifying 1728 + 12q + q2 = 0 Solving 1728 + 12q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '-1728' to each side of the equation. 1728 + 12q + -1728 + q2 = 0 + -1728 Reorder the terms: 1728 + -1728 + 12q + q2 = 0 + -1728 Combine like terms: 1728 + -1728 = 0 0 + 12q + q2 = 0 + -1728 12q + q2 = 0 + -1728 Combine like terms: 0 + -1728 = -1728 12q + q2 = -1728 The q term is 12q. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12q + 36 + q2 = -1728 + 36 Reorder the terms: 36 + 12q + q2 = -1728 + 36 Combine like terms: -1728 + 36 = -1692 36 + 12q + q2 = -1692 Factor a perfect square on the left side: (q + 6)(q + 6) = -1692 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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