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Simplifying 30q3 + 14q2 + 4q = 0 Reorder the terms: 4q + 14q2 + 30q3 = 0 Solving 4q + 14q2 + 30q3 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '2q'. 2q(2 + 7q + 15q2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'q' equal to zero and attempt to solve: Simplifying q = 0 Solving q = 0 Move all terms containing q to the left, all other terms to the right. Simplifying q = 0Subproblem 2
Set the factor '(2 + 7q + 15q2)' equal to zero and attempt to solve: Simplifying 2 + 7q + 15q2 = 0 Solving 2 + 7q + 15q2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 0.1333333333 + 0.4666666667q + q2 = 0 Move the constant term to the right: Add '-0.1333333333' to each side of the equation. 0.1333333333 + 0.4666666667q + -0.1333333333 + q2 = 0 + -0.1333333333 Reorder the terms: 0.1333333333 + -0.1333333333 + 0.4666666667q + q2 = 0 + -0.1333333333 Combine like terms: 0.1333333333 + -0.1333333333 = 0.0000000000 0.0000000000 + 0.4666666667q + q2 = 0 + -0.1333333333 0.4666666667q + q2 = 0 + -0.1333333333 Combine like terms: 0 + -0.1333333333 = -0.1333333333 0.4666666667q + q2 = -0.1333333333 The q term is 0.4666666667q. Take half its coefficient (0.2333333334). Square it (0.05444444448) and add it to both sides. Add '0.05444444448' to each side of the equation. 0.4666666667q + 0.05444444448 + q2 = -0.1333333333 + 0.05444444448 Reorder the terms: 0.05444444448 + 0.4666666667q + q2 = -0.1333333333 + 0.05444444448 Combine like terms: -0.1333333333 + 0.05444444448 = -0.07888888882 0.05444444448 + 0.4666666667q + q2 = -0.07888888882 Factor a perfect square on the left side: (q + 0.2333333334)(q + 0.2333333334) = -0.07888888882 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.Solution
q = {0}
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