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Simplifying q2 + -10q + -17 = 0 Reorder the terms: -17 + -10q + q2 = 0 Solving -17 + -10q + q2 = 0 Solving for variable 'q'. Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + -10q + 17 + q2 = 0 + 17 Reorder the terms: -17 + 17 + -10q + q2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -10q + q2 = 0 + 17 -10q + q2 = 0 + 17 Combine like terms: 0 + 17 = 17 -10q + q2 = 17 The q term is -10q. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10q + 25 + q2 = 17 + 25 Reorder the terms: 25 + -10q + q2 = 17 + 25 Combine like terms: 17 + 25 = 42 25 + -10q + q2 = 42 Factor a perfect square on the left side: (q + -5)(q + -5) = 42 Calculate the square root of the right side: 6.480740698 Break this problem into two subproblems by setting (q + -5) equal to 6.480740698 and -6.480740698.Subproblem 1
q + -5 = 6.480740698 Simplifying q + -5 = 6.480740698 Reorder the terms: -5 + q = 6.480740698 Solving -5 + q = 6.480740698 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + q = 6.480740698 + 5 Combine like terms: -5 + 5 = 0 0 + q = 6.480740698 + 5 q = 6.480740698 + 5 Combine like terms: 6.480740698 + 5 = 11.480740698 q = 11.480740698 Simplifying q = 11.480740698Subproblem 2
q + -5 = -6.480740698 Simplifying q + -5 = -6.480740698 Reorder the terms: -5 + q = -6.480740698 Solving -5 + q = -6.480740698 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + q = -6.480740698 + 5 Combine like terms: -5 + 5 = 0 0 + q = -6.480740698 + 5 q = -6.480740698 + 5 Combine like terms: -6.480740698 + 5 = -1.480740698 q = -1.480740698 Simplifying q = -1.480740698Solution
The solution to the problem is based on the solutions from the subproblems. q = {11.480740698, -1.480740698}
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