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Simplifying q2 + 6q + -19 = 0 Reorder the terms: -19 + 6q + q2 = 0 Solving -19 + 6q + q2 = 0 Solving for variable 'q'. Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + 6q + 19 + q2 = 0 + 19 Reorder the terms: -19 + 19 + 6q + q2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 6q + q2 = 0 + 19 6q + q2 = 0 + 19 Combine like terms: 0 + 19 = 19 6q + q2 = 19 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 = 19 + 9 Reorder the terms: 9 + 6q + q2 = 19 + 9 Combine like terms: 19 + 9 = 28 9 + 6q + q2 = 28 Factor a perfect square on the left side: (q + 3)(q + 3) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (q + 3) equal to 5.291502622 and -5.291502622.Subproblem 1
q + 3 = 5.291502622 Simplifying q + 3 = 5.291502622 Reorder the terms: 3 + q = 5.291502622 Solving 3 + q = 5.291502622 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 = 5.291502622 + -3 Combine like terms: 3 + -3 = 0 0 + q = 5.291502622 + -3 q = 5.291502622 + -3 Combine like terms: 5.291502622 + -3 = 2.291502622 q = 2.291502622 Simplifying q = 2.291502622Subproblem 2
q + 3 = -5.291502622 Simplifying q + 3 = -5.291502622 Reorder the terms: 3 + q = -5.291502622 Solving 3 + q = -5.291502622 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 = -5.291502622 + -3 Combine like terms: 3 + -3 = 0 0 + q = -5.291502622 + -3 q = -5.291502622 + -3 Combine like terms: -5.291502622 + -3 = -8.291502622 q = -8.291502622 Simplifying q = -8.291502622Solution
The solution to the problem is based on the solutions from the subproblems. q = {2.291502622, -8.291502622}
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