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Simplifying q2 + 17q + -72 = 0 Reorder the terms: -72 + 17q + q2 = 0 Solving -72 + 17q + q2 = 0 Solving for variable 'q'. Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + 17q + 72 + q2 = 0 + 72 Reorder the terms: -72 + 72 + 17q + q2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 17q + q2 = 0 + 72 17q + q2 = 0 + 72 Combine like terms: 0 + 72 = 72 17q + q2 = 72 The q term is 17q. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17q + 72.25 + q2 = 72 + 72.25 Reorder the terms: 72.25 + 17q + q2 = 72 + 72.25 Combine like terms: 72 + 72.25 = 144.25 72.25 + 17q + q2 = 144.25 Factor a perfect square on the left side: (q + 8.5)(q + 8.5) = 144.25 Calculate the square root of the right side: 12.010412149 Break this problem into two subproblems by setting (q + 8.5) equal to 12.010412149 and -12.010412149.Subproblem 1
q + 8.5 = 12.010412149 Simplifying q + 8.5 = 12.010412149 Reorder the terms: 8.5 + q = 12.010412149 Solving 8.5 + q = 12.010412149 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + q = 12.010412149 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + q = 12.010412149 + -8.5 q = 12.010412149 + -8.5 Combine like terms: 12.010412149 + -8.5 = 3.510412149 q = 3.510412149 Simplifying q = 3.510412149Subproblem 2
q + 8.5 = -12.010412149 Simplifying q + 8.5 = -12.010412149 Reorder the terms: 8.5 + q = -12.010412149 Solving 8.5 + q = -12.010412149 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + q = -12.010412149 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + q = -12.010412149 + -8.5 q = -12.010412149 + -8.5 Combine like terms: -12.010412149 + -8.5 = -20.510412149 q = -20.510412149 Simplifying q = -20.510412149Solution
The solution to the problem is based on the solutions from the subproblems. q = {3.510412149, -20.510412149}
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