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Simplifying q2 + 20q = -17 Reorder the terms: 20q + q2 = -17 Solving 20q + q2 = -17 Solving for variable 'q'. Reorder the terms: 17 + 20q + q2 = -17 + 17 Combine like terms: -17 + 17 = 0 17 + 20q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + 20q + -17 + q2 = 0 + -17 Reorder the terms: 17 + -17 + 20q + q2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 20q + q2 = 0 + -17 20q + q2 = 0 + -17 Combine like terms: 0 + -17 = -17 20q + q2 = -17 The q term is 20q. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20q + 100 + q2 = -17 + 100 Reorder the terms: 100 + 20q + q2 = -17 + 100 Combine like terms: -17 + 100 = 83 100 + 20q + q2 = 83 Factor a perfect square on the left side: (q + 10)(q + 10) = 83 Calculate the square root of the right side: 9.110433579 Break this problem into two subproblems by setting (q + 10) equal to 9.110433579 and -9.110433579.Subproblem 1
q + 10 = 9.110433579 Simplifying q + 10 = 9.110433579 Reorder the terms: 10 + q = 9.110433579 Solving 10 + q = 9.110433579 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + q = 9.110433579 + -10 Combine like terms: 10 + -10 = 0 0 + q = 9.110433579 + -10 q = 9.110433579 + -10 Combine like terms: 9.110433579 + -10 = -0.889566421 q = -0.889566421 Simplifying q = -0.889566421Subproblem 2
q + 10 = -9.110433579 Simplifying q + 10 = -9.110433579 Reorder the terms: 10 + q = -9.110433579 Solving 10 + q = -9.110433579 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + q = -9.110433579 + -10 Combine like terms: 10 + -10 = 0 0 + q = -9.110433579 + -10 q = -9.110433579 + -10 Combine like terms: -9.110433579 + -10 = -19.110433579 q = -19.110433579 Simplifying q = -19.110433579Solution
The solution to the problem is based on the solutions from the subproblems. q = {-0.889566421, -19.110433579}
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