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Simplifying q2 + 16q = 23 Reorder the terms: 16q + q2 = 23 Solving 16q + q2 = 23 Solving for variable 'q'. Reorder the terms: -23 + 16q + q2 = 23 + -23 Combine like terms: 23 + -23 = 0 -23 + 16q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + 16q + 23 + q2 = 0 + 23 Reorder the terms: -23 + 23 + 16q + q2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 16q + q2 = 0 + 23 16q + q2 = 0 + 23 Combine like terms: 0 + 23 = 23 16q + q2 = 23 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 = 23 + 64 Reorder the terms: 64 + 16q + q2 = 23 + 64 Combine like terms: 23 + 64 = 87 64 + 16q + q2 = 87 Factor a perfect square on the left side: (q + 8)(q + 8) = 87 Calculate the square root of the right side: 9.327379053 Break this problem into two subproblems by setting (q + 8) equal to 9.327379053 and -9.327379053.Subproblem 1
q + 8 = 9.327379053 Simplifying q + 8 = 9.327379053 Reorder the terms: 8 + q = 9.327379053 Solving 8 + q = 9.327379053 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 = 9.327379053 + -8 Combine like terms: 8 + -8 = 0 0 + q = 9.327379053 + -8 q = 9.327379053 + -8 Combine like terms: 9.327379053 + -8 = 1.327379053 q = 1.327379053 Simplifying q = 1.327379053Subproblem 2
q + 8 = -9.327379053 Simplifying q + 8 = -9.327379053 Reorder the terms: 8 + q = -9.327379053 Solving 8 + q = -9.327379053 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 = -9.327379053 + -8 Combine like terms: 8 + -8 = 0 0 + q = -9.327379053 + -8 q = -9.327379053 + -8 Combine like terms: -9.327379053 + -8 = -17.327379053 q = -17.327379053 Simplifying q = -17.327379053Solution
The solution to the problem is based on the solutions from the subproblems. q = {1.327379053, -17.327379053}
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