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Simplifying q2 + 16q = 39 Reorder the terms: 16q + q2 = 39 Solving 16q + q2 = 39 Solving for variable 'q'. Reorder the terms: -39 + 16q + q2 = 39 + -39 Combine like terms: 39 + -39 = 0 -39 + 16q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + 16q + 39 + q2 = 0 + 39 Reorder the terms: -39 + 39 + 16q + q2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + 16q + q2 = 0 + 39 16q + q2 = 0 + 39 Combine like terms: 0 + 39 = 39 16q + q2 = 39 The q term is 16q. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16q + 64 + q2 = 39 + 64 Reorder the terms: 64 + 16q + q2 = 39 + 64 Combine like terms: 39 + 64 = 103 64 + 16q + q2 = 103 Factor a perfect square on the left side: (q + 8)(q + 8) = 103 Calculate the square root of the right side: 10.148891565 Break this problem into two subproblems by setting (q + 8) equal to 10.148891565 and -10.148891565.Subproblem 1
q + 8 = 10.148891565 Simplifying q + 8 = 10.148891565 Reorder the terms: 8 + q = 10.148891565 Solving 8 + q = 10.148891565 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + q = 10.148891565 + -8 Combine like terms: 8 + -8 = 0 0 + q = 10.148891565 + -8 q = 10.148891565 + -8 Combine like terms: 10.148891565 + -8 = 2.148891565 q = 2.148891565 Simplifying q = 2.148891565Subproblem 2
q + 8 = -10.148891565 Simplifying q + 8 = -10.148891565 Reorder the terms: 8 + q = -10.148891565 Solving 8 + q = -10.148891565 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + q = -10.148891565 + -8 Combine like terms: 8 + -8 = 0 0 + q = -10.148891565 + -8 q = -10.148891565 + -8 Combine like terms: -10.148891565 + -8 = -18.148891565 q = -18.148891565 Simplifying q = -18.148891565Solution
The solution to the problem is based on the solutions from the subproblems. q = {2.148891565, -18.148891565}
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