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Simplifying 9q + 3q(q + -7) = 18 + -1q Reorder the terms: 9q + 3q(-7 + q) = 18 + -1q 9q + (-7 * 3q + q * 3q) = 18 + -1q 9q + (-21q + 3q2) = 18 + -1q Combine like terms: 9q + -21q = -12q -12q + 3q2 = 18 + -1q Solving -12q + 3q2 = 18 + -1q Solving for variable 'q'. Reorder the terms: -18 + -12q + q + 3q2 = 18 + -1q + -18 + q Combine like terms: -12q + q = -11q -18 + -11q + 3q2 = 18 + -1q + -18 + q Reorder the terms: -18 + -11q + 3q2 = 18 + -18 + -1q + q Combine like terms: 18 + -18 = 0 -18 + -11q + 3q2 = 0 + -1q + q -18 + -11q + 3q2 = -1q + q Combine like terms: -1q + q = 0 -18 + -11q + 3q2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -6 + -3.666666667q + q2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -3.666666667q + 6 + q2 = 0 + 6 Reorder the terms: -6 + 6 + -3.666666667q + q2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -3.666666667q + q2 = 0 + 6 -3.666666667q + q2 = 0 + 6 Combine like terms: 0 + 6 = 6 -3.666666667q + q2 = 6 The q term is -3.666666667q. Take half its coefficient (-1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. -3.666666667q + 3.361111114 + q2 = 6 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667q + q2 = 6 + 3.361111114 Combine like terms: 6 + 3.361111114 = 9.361111114 3.361111114 + -3.666666667q + q2 = 9.361111114 Factor a perfect square on the left side: (q + -1.833333334)(q + -1.833333334) = 9.361111114 Calculate the square root of the right side: 3.059593292 Break this problem into two subproblems by setting (q + -1.833333334) equal to 3.059593292 and -3.059593292.Subproblem 1
q + -1.833333334 = 3.059593292 Simplifying q + -1.833333334 = 3.059593292 Reorder the terms: -1.833333334 + q = 3.059593292 Solving -1.833333334 + q = 3.059593292 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + q = 3.059593292 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + q = 3.059593292 + 1.833333334 q = 3.059593292 + 1.833333334 Combine like terms: 3.059593292 + 1.833333334 = 4.892926626 q = 4.892926626 Simplifying q = 4.892926626Subproblem 2
q + -1.833333334 = -3.059593292 Simplifying q + -1.833333334 = -3.059593292 Reorder the terms: -1.833333334 + q = -3.059593292 Solving -1.833333334 + q = -3.059593292 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + q = -3.059593292 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + q = -3.059593292 + 1.833333334 q = -3.059593292 + 1.833333334 Combine like terms: -3.059593292 + 1.833333334 = -1.226259958 q = -1.226259958 Simplifying q = -1.226259958Solution
The solution to the problem is based on the solutions from the subproblems. q = {4.892926626, -1.226259958}
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