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Simplifying q2 + -4q = 43 Reorder the terms: -4q + q2 = 43 Solving -4q + q2 = 43 Solving for variable 'q'. Reorder the terms: -43 + -4q + q2 = 43 + -43 Combine like terms: 43 + -43 = 0 -43 + -4q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + -4q + 43 + q2 = 0 + 43 Reorder the terms: -43 + 43 + -4q + q2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + -4q + q2 = 0 + 43 -4q + q2 = 0 + 43 Combine like terms: 0 + 43 = 43 -4q + q2 = 43 The q term is -4q. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4q + 4 + q2 = 43 + 4 Reorder the terms: 4 + -4q + q2 = 43 + 4 Combine like terms: 43 + 4 = 47 4 + -4q + q2 = 47 Factor a perfect square on the left side: (q + -2)(q + -2) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (q + -2) equal to 6.8556546 and -6.8556546.Subproblem 1
q + -2 = 6.8556546 Simplifying q + -2 = 6.8556546 Reorder the terms: -2 + q = 6.8556546 Solving -2 + q = 6.8556546 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + q = 6.8556546 + 2 Combine like terms: -2 + 2 = 0 0 + q = 6.8556546 + 2 q = 6.8556546 + 2 Combine like terms: 6.8556546 + 2 = 8.8556546 q = 8.8556546 Simplifying q = 8.8556546Subproblem 2
q + -2 = -6.8556546 Simplifying q + -2 = -6.8556546 Reorder the terms: -2 + q = -6.8556546 Solving -2 + q = -6.8556546 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + q = -6.8556546 + 2 Combine like terms: -2 + 2 = 0 0 + q = -6.8556546 + 2 q = -6.8556546 + 2 Combine like terms: -6.8556546 + 2 = -4.8556546 q = -4.8556546 Simplifying q = -4.8556546Solution
The solution to the problem is based on the solutions from the subproblems. q = {8.8556546, -4.8556546}
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