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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 = 20.5625 18.0625 + -8.5q + q2 = 20.5625 Factor a perfect square on the left side: (q + -4.25)(q + -4.25) = 20.5625 Calculate the square root of the right side: 4.534589287 Break this problem into two subproblems by setting (q + -4.25) equal to 4.534589287 and -4.534589287.Subproblem 1
q + -4.25 = 4.534589287 Simplifying q + -4.25 = 4.534589287 Reorder the terms: -4.25 + q = 4.534589287 Solving -4.25 + q = 4.534589287 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 = 4.534589287 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + q = 4.534589287 + 4.25 q = 4.534589287 + 4.25 Combine like terms: 4.534589287 + 4.25 = 8.784589287 q = 8.784589287 Simplifying q = 8.784589287Subproblem 2
q + -4.25 = -4.534589287 Simplifying q + -4.25 = -4.534589287 Reorder the terms: -4.25 + q = -4.534589287 Solving -4.25 + q = -4.534589287 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 = -4.534589287 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + q = -4.534589287 + 4.25 q = -4.534589287 + 4.25 Combine like terms: -4.534589287 + 4.25 = -0.284589287 q = -0.284589287 Simplifying q = -0.284589287Solution
The solution to the problem is based on the solutions from the subproblems. q = {8.784589287, -0.284589287}
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