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Simplifying q2 + 2q + -16 = 0 Reorder the terms: -16 + 2q + q2 = 0 Solving -16 + 2q + q2 = 0 Solving for variable 'q'. Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 2q + 16 + q2 = 0 + 16 Reorder the terms: -16 + 16 + 2q + q2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 2q + q2 = 0 + 16 2q + q2 = 0 + 16 Combine like terms: 0 + 16 = 16 2q + q2 = 16 The q term is 2q. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2q + 1 + q2 = 16 + 1 Reorder the terms: 1 + 2q + q2 = 16 + 1 Combine like terms: 16 + 1 = 17 1 + 2q + q2 = 17 Factor a perfect square on the left side: (q + 1)(q + 1) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (q + 1) equal to 4.123105626 and -4.123105626.Subproblem 1
q + 1 = 4.123105626 Simplifying q + 1 = 4.123105626 Reorder the terms: 1 + q = 4.123105626 Solving 1 + q = 4.123105626 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + q = 4.123105626 + -1 Combine like terms: 1 + -1 = 0 0 + q = 4.123105626 + -1 q = 4.123105626 + -1 Combine like terms: 4.123105626 + -1 = 3.123105626 q = 3.123105626 Simplifying q = 3.123105626Subproblem 2
q + 1 = -4.123105626 Simplifying q + 1 = -4.123105626 Reorder the terms: 1 + q = -4.123105626 Solving 1 + q = -4.123105626 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + q = -4.123105626 + -1 Combine like terms: 1 + -1 = 0 0 + q = -4.123105626 + -1 q = -4.123105626 + -1 Combine like terms: -4.123105626 + -1 = -5.123105626 q = -5.123105626 Simplifying q = -5.123105626Solution
The solution to the problem is based on the solutions from the subproblems. q = {3.123105626, -5.123105626}
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