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Simplifying 3q2 + -12q + 18 = 20 Reorder the terms: 18 + -12q + 3q2 = 20 Solving 18 + -12q + 3q2 = 20 Solving for variable 'q'. Reorder the terms: 18 + -20 + -12q + 3q2 = 20 + -20 Combine like terms: 18 + -20 = -2 -2 + -12q + 3q2 = 20 + -20 Combine like terms: 20 + -20 = 0 -2 + -12q + 3q2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.6666666667 + -4q + q2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -4q + 0.6666666667 + q2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -4q + q2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -4q + q2 = 0 + 0.6666666667 -4q + q2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -4q + q2 = 0.6666666667 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 = 0.6666666667 + 4 Reorder the terms: 4 + -4q + q2 = 0.6666666667 + 4 Combine like terms: 0.6666666667 + 4 = 4.6666666667 4 + -4q + q2 = 4.6666666667 Factor a perfect square on the left side: (q + -2)(q + -2) = 4.6666666667 Calculate the square root of the right side: 2.160246899 Break this problem into two subproblems by setting (q + -2) equal to 2.160246899 and -2.160246899.Subproblem 1
q + -2 = 2.160246899 Simplifying q + -2 = 2.160246899 Reorder the terms: -2 + q = 2.160246899 Solving -2 + q = 2.160246899 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + q = 2.160246899 + 2 Combine like terms: -2 + 2 = 0 0 + q = 2.160246899 + 2 q = 2.160246899 + 2 Combine like terms: 2.160246899 + 2 = 4.160246899 q = 4.160246899 Simplifying q = 4.160246899Subproblem 2
q + -2 = -2.160246899 Simplifying q + -2 = -2.160246899 Reorder the terms: -2 + q = -2.160246899 Solving -2 + q = -2.160246899 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + q = -2.160246899 + 2 Combine like terms: -2 + 2 = 0 0 + q = -2.160246899 + 2 q = -2.160246899 + 2 Combine like terms: -2.160246899 + 2 = -0.160246899 q = -0.160246899 Simplifying q = -0.160246899Solution
The solution to the problem is based on the solutions from the subproblems. q = {4.160246899, -0.160246899}
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