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Simplifying 3q3 + 14q2 + -4q = 0 Reorder the terms: -4q + 14q2 + 3q3 = 0 Solving -4q + 14q2 + 3q3 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), 'q'. q(-4 + 14q + 3q2) = 0Subproblem 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 '(-4 + 14q + 3q2)' equal to zero and attempt to solve: Simplifying -4 + 14q + 3q2 = 0 Solving -4 + 14q + 3q2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.333333333 + 4.666666667q + q2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 4.666666667q + 1.333333333 + q2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 4.666666667q + q2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 4.666666667q + q2 = 0 + 1.333333333 4.666666667q + q2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 4.666666667q + q2 = 1.333333333 The q term is 4.666666667q. Take half its coefficient (2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. 4.666666667q + 5.444444448 + q2 = 1.333333333 + 5.444444448 Reorder the terms: 5.444444448 + 4.666666667q + q2 = 1.333333333 + 5.444444448 Combine like terms: 1.333333333 + 5.444444448 = 6.777777781 5.444444448 + 4.666666667q + q2 = 6.777777781 Factor a perfect square on the left side: (q + 2.333333334)(q + 2.333333334) = 6.777777781 Calculate the square root of the right side: 2.603416559 Break this problem into two subproblems by setting (q + 2.333333334) equal to 2.603416559 and -2.603416559.Subproblem 1
q + 2.333333334 = 2.603416559 Simplifying q + 2.333333334 = 2.603416559 Reorder the terms: 2.333333334 + q = 2.603416559 Solving 2.333333334 + q = 2.603416559 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + q = 2.603416559 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + q = 2.603416559 + -2.333333334 q = 2.603416559 + -2.333333334 Combine like terms: 2.603416559 + -2.333333334 = 0.270083225 q = 0.270083225 Simplifying q = 0.270083225Subproblem 2
q + 2.333333334 = -2.603416559 Simplifying q + 2.333333334 = -2.603416559 Reorder the terms: 2.333333334 + q = -2.603416559 Solving 2.333333334 + q = -2.603416559 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + q = -2.603416559 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + q = -2.603416559 + -2.333333334 q = -2.603416559 + -2.333333334 Combine like terms: -2.603416559 + -2.333333334 = -4.936749893 q = -4.936749893 Simplifying q = -4.936749893Solution
The solution to the problem is based on the solutions from the subproblems. q = {0.270083225, -4.936749893}Solution
q = {0, 0.270083225, -4.936749893}
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