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Simplifying 5q2 + 20q + 30 = 0 Reorder the terms: 30 + 20q + 5q2 = 0 Solving 30 + 20q + 5q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '5'. 5(6 + 4q + q2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(6 + 4q + q2)' equal to zero and attempt to solve: Simplifying 6 + 4q + q2 = 0 Solving 6 + 4q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 4q + -6 + q2 = 0 + -6 Reorder the terms: 6 + -6 + 4q + q2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 4q + q2 = 0 + -6 4q + q2 = 0 + -6 Combine like terms: 0 + -6 = -6 4q + q2 = -6 The q term is 4q. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4q + 4 + q2 = -6 + 4 Reorder the terms: 4 + 4q + q2 = -6 + 4 Combine like terms: -6 + 4 = -2 4 + 4q + q2 = -2 Factor a perfect square on the left side: (q + 2)(q + 2) = -2 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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