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Simplifying q2 + 4q = 49 Reorder the terms: 4q + q2 = 49 Solving 4q + q2 = 49 Solving for variable 'q'. Reorder the terms: -49 + 4q + q2 = 49 + -49 Combine like terms: 49 + -49 = 0 -49 + 4q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + 4q + 49 + q2 = 0 + 49 Reorder the terms: -49 + 49 + 4q + q2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 4q + q2 = 0 + 49 4q + q2 = 0 + 49 Combine like terms: 0 + 49 = 49 4q + q2 = 49 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 = 49 + 4 Reorder the terms: 4 + 4q + q2 = 49 + 4 Combine like terms: 49 + 4 = 53 4 + 4q + q2 = 53 Factor a perfect square on the left side: (q + 2)(q + 2) = 53 Calculate the square root of the right side: 7.280109889 Break this problem into two subproblems by setting (q + 2) equal to 7.280109889 and -7.280109889.Subproblem 1
q + 2 = 7.280109889 Simplifying q + 2 = 7.280109889 Reorder the terms: 2 + q = 7.280109889 Solving 2 + q = 7.280109889 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 = 7.280109889 + -2 Combine like terms: 2 + -2 = 0 0 + q = 7.280109889 + -2 q = 7.280109889 + -2 Combine like terms: 7.280109889 + -2 = 5.280109889 q = 5.280109889 Simplifying q = 5.280109889Subproblem 2
q + 2 = -7.280109889 Simplifying q + 2 = -7.280109889 Reorder the terms: 2 + q = -7.280109889 Solving 2 + q = -7.280109889 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 = -7.280109889 + -2 Combine like terms: 2 + -2 = 0 0 + q = -7.280109889 + -2 q = -7.280109889 + -2 Combine like terms: -7.280109889 + -2 = -9.280109889 q = -9.280109889 Simplifying q = -9.280109889Solution
The solution to the problem is based on the solutions from the subproblems. q = {5.280109889, -9.280109889}
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