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Simplifying q2 + 18q = -47 Reorder the terms: 18q + q2 = -47 Solving 18q + q2 = -47 Solving for variable 'q'. Reorder the terms: 47 + 18q + q2 = -47 + 47 Combine like terms: -47 + 47 = 0 47 + 18q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '-47' to each side of the equation. 47 + 18q + -47 + q2 = 0 + -47 Reorder the terms: 47 + -47 + 18q + q2 = 0 + -47 Combine like terms: 47 + -47 = 0 0 + 18q + q2 = 0 + -47 18q + q2 = 0 + -47 Combine like terms: 0 + -47 = -47 18q + q2 = -47 The q term is 18q. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18q + 81 + q2 = -47 + 81 Reorder the terms: 81 + 18q + q2 = -47 + 81 Combine like terms: -47 + 81 = 34 81 + 18q + q2 = 34 Factor a perfect square on the left side: (q + 9)(q + 9) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (q + 9) equal to 5.830951895 and -5.830951895.Subproblem 1
q + 9 = 5.830951895 Simplifying q + 9 = 5.830951895 Reorder the terms: 9 + q = 5.830951895 Solving 9 + q = 5.830951895 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + q = 5.830951895 + -9 Combine like terms: 9 + -9 = 0 0 + q = 5.830951895 + -9 q = 5.830951895 + -9 Combine like terms: 5.830951895 + -9 = -3.169048105 q = -3.169048105 Simplifying q = -3.169048105Subproblem 2
q + 9 = -5.830951895 Simplifying q + 9 = -5.830951895 Reorder the terms: 9 + q = -5.830951895 Solving 9 + q = -5.830951895 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + q = -5.830951895 + -9 Combine like terms: 9 + -9 = 0 0 + q = -5.830951895 + -9 q = -5.830951895 + -9 Combine like terms: -5.830951895 + -9 = -14.830951895 q = -14.830951895 Simplifying q = -14.830951895Solution
The solution to the problem is based on the solutions from the subproblems. q = {-3.169048105, -14.830951895}
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