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Simplifying 0 = -1q2 + 8q + 41 Reorder the terms: 0 = 41 + 8q + -1q2 Solving 0 = 41 + 8q + -1q2 Solving for variable 'q'. Combine like terms: 0 + -41 = -41 -41 + -8q + q2 = 41 + 8q + -1q2 + -41 + -8q + q2 Reorder the terms: -41 + -8q + q2 = 41 + -41 + 8q + -8q + -1q2 + q2 Combine like terms: 41 + -41 = 0 -41 + -8q + q2 = 0 + 8q + -8q + -1q2 + q2 -41 + -8q + q2 = 8q + -8q + -1q2 + q2 Combine like terms: 8q + -8q = 0 -41 + -8q + q2 = 0 + -1q2 + q2 -41 + -8q + q2 = -1q2 + q2 Combine like terms: -1q2 + q2 = 0 -41 + -8q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + -8q + 41 + q2 = 0 + 41 Reorder the terms: -41 + 41 + -8q + q2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + -8q + q2 = 0 + 41 -8q + q2 = 0 + 41 Combine like terms: 0 + 41 = 41 -8q + q2 = 41 The q term is -8q. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8q + 16 + q2 = 41 + 16 Reorder the terms: 16 + -8q + q2 = 41 + 16 Combine like terms: 41 + 16 = 57 16 + -8q + q2 = 57 Factor a perfect square on the left side: (q + -4)(q + -4) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (q + -4) equal to 7.549834435 and -7.549834435.Subproblem 1
q + -4 = 7.549834435 Simplifying q + -4 = 7.549834435 Reorder the terms: -4 + q = 7.549834435 Solving -4 + q = 7.549834435 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + q = 7.549834435 + 4 Combine like terms: -4 + 4 = 0 0 + q = 7.549834435 + 4 q = 7.549834435 + 4 Combine like terms: 7.549834435 + 4 = 11.549834435 q = 11.549834435 Simplifying q = 11.549834435Subproblem 2
q + -4 = -7.549834435 Simplifying q + -4 = -7.549834435 Reorder the terms: -4 + q = -7.549834435 Solving -4 + q = -7.549834435 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + q = -7.549834435 + 4 Combine like terms: -4 + 4 = 0 0 + q = -7.549834435 + 4 q = -7.549834435 + 4 Combine like terms: -7.549834435 + 4 = -3.549834435 q = -3.549834435 Simplifying q = -3.549834435Solution
The solution to the problem is based on the solutions from the subproblems. q = {11.549834435, -3.549834435}
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