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Simplifying (q + -1)(q + -3) = 2 Reorder the terms: (-1 + q)(q + -3) = 2 Reorder the terms: (-1 + q)(-3 + q) = 2 Multiply (-1 + q) * (-3 + q) (-1(-3 + q) + q(-3 + q)) = 2 ((-3 * -1 + q * -1) + q(-3 + q)) = 2 ((3 + -1q) + q(-3 + q)) = 2 (3 + -1q + (-3 * q + q * q)) = 2 (3 + -1q + (-3q + q2)) = 2 Combine like terms: -1q + -3q = -4q (3 + -4q + q2) = 2 Solving 3 + -4q + q2 = 2 Solving for variable 'q'. Reorder the terms: 3 + -2 + -4q + q2 = 2 + -2 Combine like terms: 3 + -2 = 1 1 + -4q + q2 = 2 + -2 Combine like terms: 2 + -2 = 0 1 + -4q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -4q + -1 + q2 = 0 + -1 Reorder the terms: 1 + -1 + -4q + q2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4q + q2 = 0 + -1 -4q + q2 = 0 + -1 Combine like terms: 0 + -1 = -1 -4q + q2 = -1 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 = -1 + 4 Reorder the terms: 4 + -4q + q2 = -1 + 4 Combine like terms: -1 + 4 = 3 4 + -4q + q2 = 3 Factor a perfect square on the left side: (q + -2)(q + -2) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (q + -2) equal to 1.732050808 and -1.732050808.Subproblem 1
q + -2 = 1.732050808 Simplifying q + -2 = 1.732050808 Reorder the terms: -2 + q = 1.732050808 Solving -2 + q = 1.732050808 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 = 1.732050808 + 2 Combine like terms: -2 + 2 = 0 0 + q = 1.732050808 + 2 q = 1.732050808 + 2 Combine like terms: 1.732050808 + 2 = 3.732050808 q = 3.732050808 Simplifying q = 3.732050808Subproblem 2
q + -2 = -1.732050808 Simplifying q + -2 = -1.732050808 Reorder the terms: -2 + q = -1.732050808 Solving -2 + q = -1.732050808 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 = -1.732050808 + 2 Combine like terms: -2 + 2 = 0 0 + q = -1.732050808 + 2 q = -1.732050808 + 2 Combine like terms: -1.732050808 + 2 = 0.267949192 q = 0.267949192 Simplifying q = 0.267949192Solution
The solution to the problem is based on the solutions from the subproblems. q = {3.732050808, 0.267949192}
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