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Simplifying q2 + -1q + -41 = 0 Reorder the terms: -41 + -1q + q2 = 0 Solving -41 + -1q + q2 = 0 Solving for variable 'q'. Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + -1q + 41 + q2 = 0 + 41 Reorder the terms: -41 + 41 + -1q + q2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + -1q + q2 = 0 + 41 -1q + q2 = 0 + 41 Combine like terms: 0 + 41 = 41 -1q + q2 = 41 The q term is -1q. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1q + 0.25 + q2 = 41 + 0.25 Reorder the terms: 0.25 + -1q + q2 = 41 + 0.25 Combine like terms: 41 + 0.25 = 41.25 0.25 + -1q + q2 = 41.25 Factor a perfect square on the left side: (q + -0.5)(q + -0.5) = 41.25 Calculate the square root of the right side: 6.422616289 Break this problem into two subproblems by setting (q + -0.5) equal to 6.422616289 and -6.422616289.Subproblem 1
q + -0.5 = 6.422616289 Simplifying q + -0.5 = 6.422616289 Reorder the terms: -0.5 + q = 6.422616289 Solving -0.5 + q = 6.422616289 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + q = 6.422616289 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + q = 6.422616289 + 0.5 q = 6.422616289 + 0.5 Combine like terms: 6.422616289 + 0.5 = 6.922616289 q = 6.922616289 Simplifying q = 6.922616289Subproblem 2
q + -0.5 = -6.422616289 Simplifying q + -0.5 = -6.422616289 Reorder the terms: -0.5 + q = -6.422616289 Solving -0.5 + q = -6.422616289 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + q = -6.422616289 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + q = -6.422616289 + 0.5 q = -6.422616289 + 0.5 Combine like terms: -6.422616289 + 0.5 = -5.922616289 q = -5.922616289 Simplifying q = -5.922616289Solution
The solution to the problem is based on the solutions from the subproblems. q = {6.922616289, -5.922616289}
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