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Simplifying q2 + 4q = 16 Reorder the terms: 4q + q2 = 16 Solving 4q + q2 = 16 Solving for variable 'q'. Reorder the terms: -16 + 4q + q2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + 4q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 4q + 16 + q2 = 0 + 16 Reorder the terms: -16 + 16 + 4q + q2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 4q + q2 = 0 + 16 4q + q2 = 0 + 16 Combine like terms: 0 + 16 = 16 4q + q2 = 16 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 = 16 + 4 Reorder the terms: 4 + 4q + q2 = 16 + 4 Combine like terms: 16 + 4 = 20 4 + 4q + q2 = 20 Factor a perfect square on the left side: (q + 2)(q + 2) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (q + 2) equal to 4.472135955 and -4.472135955.Subproblem 1
q + 2 = 4.472135955 Simplifying q + 2 = 4.472135955 Reorder the terms: 2 + q = 4.472135955 Solving 2 + q = 4.472135955 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 = 4.472135955 + -2 Combine like terms: 2 + -2 = 0 0 + q = 4.472135955 + -2 q = 4.472135955 + -2 Combine like terms: 4.472135955 + -2 = 2.472135955 q = 2.472135955 Simplifying q = 2.472135955Subproblem 2
q + 2 = -4.472135955 Simplifying q + 2 = -4.472135955 Reorder the terms: 2 + q = -4.472135955 Solving 2 + q = -4.472135955 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 = -4.472135955 + -2 Combine like terms: 2 + -2 = 0 0 + q = -4.472135955 + -2 q = -4.472135955 + -2 Combine like terms: -4.472135955 + -2 = -6.472135955 q = -6.472135955 Simplifying q = -6.472135955Solution
The solution to the problem is based on the solutions from the subproblems. q = {2.472135955, -6.472135955}
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