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Simplifying q2 = -10q + 3 Reorder the terms: q2 = 3 + -10q Solving q2 = 3 + -10q Solving for variable 'q'. Reorder the terms: -3 + 10q + q2 = 3 + -10q + -3 + 10q Reorder the terms: -3 + 10q + q2 = 3 + -3 + -10q + 10q Combine like terms: 3 + -3 = 0 -3 + 10q + q2 = 0 + -10q + 10q -3 + 10q + q2 = -10q + 10q Combine like terms: -10q + 10q = 0 -3 + 10q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 10q + 3 + q2 = 0 + 3 Reorder the terms: -3 + 3 + 10q + q2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 10q + q2 = 0 + 3 10q + q2 = 0 + 3 Combine like terms: 0 + 3 = 3 10q + q2 = 3 The q term is 10q. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10q + 25 + q2 = 3 + 25 Reorder the terms: 25 + 10q + q2 = 3 + 25 Combine like terms: 3 + 25 = 28 25 + 10q + q2 = 28 Factor a perfect square on the left side: (q + 5)(q + 5) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (q + 5) equal to 5.291502622 and -5.291502622.Subproblem 1
q + 5 = 5.291502622 Simplifying q + 5 = 5.291502622 Reorder the terms: 5 + q = 5.291502622 Solving 5 + q = 5.291502622 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + q = 5.291502622 + -5 Combine like terms: 5 + -5 = 0 0 + q = 5.291502622 + -5 q = 5.291502622 + -5 Combine like terms: 5.291502622 + -5 = 0.291502622 q = 0.291502622 Simplifying q = 0.291502622Subproblem 2
q + 5 = -5.291502622 Simplifying q + 5 = -5.291502622 Reorder the terms: 5 + q = -5.291502622 Solving 5 + q = -5.291502622 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + q = -5.291502622 + -5 Combine like terms: 5 + -5 = 0 0 + q = -5.291502622 + -5 q = -5.291502622 + -5 Combine like terms: -5.291502622 + -5 = -10.291502622 q = -10.291502622 Simplifying q = -10.291502622Solution
The solution to the problem is based on the solutions from the subproblems. q = {0.291502622, -10.291502622}
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