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Simplifying 2q2 + 17q + 5 = 0 Reorder the terms: 5 + 17q + 2q2 = 0 Solving 5 + 17q + 2q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + 8.5q + q2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 8.5q + -2.5 + q2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 8.5q + q2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 8.5q + q2 = 0 + -2.5 8.5q + q2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 8.5q + q2 = -2.5 The q term is 8.5q. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5q + 18.0625 + q2 = -2.5 + 18.0625 Reorder the terms: 18.0625 + 8.5q + q2 = -2.5 + 18.0625 Combine like terms: -2.5 + 18.0625 = 15.5625 18.0625 + 8.5q + q2 = 15.5625 Factor a perfect square on the left side: (q + 4.25)(q + 4.25) = 15.5625 Calculate the square root of the right side: 3.94493346 Break this problem into two subproblems by setting (q + 4.25) equal to 3.94493346 and -3.94493346.Subproblem 1
q + 4.25 = 3.94493346 Simplifying q + 4.25 = 3.94493346 Reorder the terms: 4.25 + q = 3.94493346 Solving 4.25 + q = 3.94493346 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + q = 3.94493346 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + q = 3.94493346 + -4.25 q = 3.94493346 + -4.25 Combine like terms: 3.94493346 + -4.25 = -0.30506654 q = -0.30506654 Simplifying q = -0.30506654Subproblem 2
q + 4.25 = -3.94493346 Simplifying q + 4.25 = -3.94493346 Reorder the terms: 4.25 + q = -3.94493346 Solving 4.25 + q = -3.94493346 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + q = -3.94493346 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + q = -3.94493346 + -4.25 q = -3.94493346 + -4.25 Combine like terms: -3.94493346 + -4.25 = -8.19493346 q = -8.19493346 Simplifying q = -8.19493346Solution
The solution to the problem is based on the solutions from the subproblems. q = {-0.30506654, -8.19493346}
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