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Simplifying q2 + -11q + -16 = 0 Reorder the terms: -16 + -11q + q2 = 0 Solving -16 + -11q + 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 + -11q + 16 + q2 = 0 + 16 Reorder the terms: -16 + 16 + -11q + q2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -11q + q2 = 0 + 16 -11q + q2 = 0 + 16 Combine like terms: 0 + 16 = 16 -11q + q2 = 16 The q term is -11q. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11q + 30.25 + q2 = 16 + 30.25 Reorder the terms: 30.25 + -11q + q2 = 16 + 30.25 Combine like terms: 16 + 30.25 = 46.25 30.25 + -11q + q2 = 46.25 Factor a perfect square on the left side: (q + -5.5)(q + -5.5) = 46.25 Calculate the square root of the right side: 6.800735254 Break this problem into two subproblems by setting (q + -5.5) equal to 6.800735254 and -6.800735254.Subproblem 1
q + -5.5 = 6.800735254 Simplifying q + -5.5 = 6.800735254 Reorder the terms: -5.5 + q = 6.800735254 Solving -5.5 + q = 6.800735254 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + q = 6.800735254 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + q = 6.800735254 + 5.5 q = 6.800735254 + 5.5 Combine like terms: 6.800735254 + 5.5 = 12.300735254 q = 12.300735254 Simplifying q = 12.300735254Subproblem 2
q + -5.5 = -6.800735254 Simplifying q + -5.5 = -6.800735254 Reorder the terms: -5.5 + q = -6.800735254 Solving -5.5 + q = -6.800735254 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + q = -6.800735254 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + q = -6.800735254 + 5.5 q = -6.800735254 + 5.5 Combine like terms: -6.800735254 + 5.5 = -1.300735254 q = -1.300735254 Simplifying q = -1.300735254Solution
The solution to the problem is based on the solutions from the subproblems. q = {12.300735254, -1.300735254}
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