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Simplifying q2 + 6q + -5 = 0 Reorder the terms: -5 + 6q + q2 = 0 Solving -5 + 6q + q2 = 0 Solving for variable 'q'. Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 6q + 5 + q2 = 0 + 5 Reorder the terms: -5 + 5 + 6q + q2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 6q + q2 = 0 + 5 6q + q2 = 0 + 5 Combine like terms: 0 + 5 = 5 6q + q2 = 5 The q term is 6q. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6q + 9 + q2 = 5 + 9 Reorder the terms: 9 + 6q + q2 = 5 + 9 Combine like terms: 5 + 9 = 14 9 + 6q + q2 = 14 Factor a perfect square on the left side: (q + 3)(q + 3) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (q + 3) equal to 3.741657387 and -3.741657387.Subproblem 1
q + 3 = 3.741657387 Simplifying q + 3 = 3.741657387 Reorder the terms: 3 + q = 3.741657387 Solving 3 + q = 3.741657387 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + q = 3.741657387 + -3 Combine like terms: 3 + -3 = 0 0 + q = 3.741657387 + -3 q = 3.741657387 + -3 Combine like terms: 3.741657387 + -3 = 0.741657387 q = 0.741657387 Simplifying q = 0.741657387Subproblem 2
q + 3 = -3.741657387 Simplifying q + 3 = -3.741657387 Reorder the terms: 3 + q = -3.741657387 Solving 3 + q = -3.741657387 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + q = -3.741657387 + -3 Combine like terms: 3 + -3 = 0 0 + q = -3.741657387 + -3 q = -3.741657387 + -3 Combine like terms: -3.741657387 + -3 = -6.741657387 q = -6.741657387 Simplifying q = -6.741657387Solution
The solution to the problem is based on the solutions from the subproblems. q = {0.741657387, -6.741657387}
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