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Simplifying 19q + 17 + q2 = 0 Reorder the terms: 17 + 19q + q2 = 0 Solving 17 + 19q + q2 = 0 Solving for variable 'q'. Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + 19q + -17 + q2 = 0 + -17 Reorder the terms: 17 + -17 + 19q + q2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 19q + q2 = 0 + -17 19q + q2 = 0 + -17 Combine like terms: 0 + -17 = -17 19q + q2 = -17 The q term is 19q. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19q + 90.25 + q2 = -17 + 90.25 Reorder the terms: 90.25 + 19q + q2 = -17 + 90.25 Combine like terms: -17 + 90.25 = 73.25 90.25 + 19q + q2 = 73.25 Factor a perfect square on the left side: (q + 9.5)(q + 9.5) = 73.25 Calculate the square root of the right side: 8.558621384 Break this problem into two subproblems by setting (q + 9.5) equal to 8.558621384 and -8.558621384.Subproblem 1
q + 9.5 = 8.558621384 Simplifying q + 9.5 = 8.558621384 Reorder the terms: 9.5 + q = 8.558621384 Solving 9.5 + q = 8.558621384 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + q = 8.558621384 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + q = 8.558621384 + -9.5 q = 8.558621384 + -9.5 Combine like terms: 8.558621384 + -9.5 = -0.941378616 q = -0.941378616 Simplifying q = -0.941378616Subproblem 2
q + 9.5 = -8.558621384 Simplifying q + 9.5 = -8.558621384 Reorder the terms: 9.5 + q = -8.558621384 Solving 9.5 + q = -8.558621384 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + q = -8.558621384 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + q = -8.558621384 + -9.5 q = -8.558621384 + -9.5 Combine like terms: -8.558621384 + -9.5 = -18.058621384 q = -18.058621384 Simplifying q = -18.058621384Solution
The solution to the problem is based on the solutions from the subproblems. q = {-0.941378616, -18.058621384}
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