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Simplifying 110.0 + -0.20q = 0.01q2 + 5.50 Reorder the terms: 110.0 + -0.20q = 5.50 + 0.01q2 Solving 110.0 + -0.20q = 5.50 + 0.01q2 Solving for variable 'q'. Reorder the terms: 110.0 + -5.50 + -0.20q + -0.01q2 = 5.50 + 0.01q2 + -5.50 + -0.01q2 Combine like terms: 110.0 + -5.50 = 104.5 104.5 + -0.20q + -0.01q2 = 5.50 + 0.01q2 + -5.50 + -0.01q2 Reorder the terms: 104.5 + -0.20q + -0.01q2 = 5.50 + -5.50 + 0.01q2 + -0.01q2 Combine like terms: 5.50 + -5.50 = 0.00 104.5 + -0.20q + -0.01q2 = 0.00 + 0.01q2 + -0.01q2 104.5 + -0.20q + -0.01q2 = 0.01q2 + -0.01q2 Combine like terms: 0.01q2 + -0.01q2 = 0.00 104.5 + -0.20q + -0.01q2 = 0.00 Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. -10450 + 20q + q2 = 0 Move the constant term to the right: Add '10450' to each side of the equation. -10450 + 20q + 10450 + q2 = 0 + 10450 Reorder the terms: -10450 + 10450 + 20q + q2 = 0 + 10450 Combine like terms: -10450 + 10450 = 0 0 + 20q + q2 = 0 + 10450 20q + q2 = 0 + 10450 Combine like terms: 0 + 10450 = 10450 20q + q2 = 10450 The q term is 20q. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20q + 100 + q2 = 10450 + 100 Reorder the terms: 100 + 20q + q2 = 10450 + 100 Combine like terms: 10450 + 100 = 10550 100 + 20q + q2 = 10550 Factor a perfect square on the left side: (q + 10)(q + 10) = 10550 Calculate the square root of the right side: 102.713192921 Break this problem into two subproblems by setting (q + 10) equal to 102.713192921 and -102.713192921.Subproblem 1
q + 10 = 102.713192921 Simplifying q + 10 = 102.713192921 Reorder the terms: 10 + q = 102.713192921 Solving 10 + q = 102.713192921 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + q = 102.713192921 + -10 Combine like terms: 10 + -10 = 0 0 + q = 102.713192921 + -10 q = 102.713192921 + -10 Combine like terms: 102.713192921 + -10 = 92.713192921 q = 92.713192921 Simplifying q = 92.713192921Subproblem 2
q + 10 = -102.713192921 Simplifying q + 10 = -102.713192921 Reorder the terms: 10 + q = -102.713192921 Solving 10 + q = -102.713192921 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + q = -102.713192921 + -10 Combine like terms: 10 + -10 = 0 0 + q = -102.713192921 + -10 q = -102.713192921 + -10 Combine like terms: -102.713192921 + -10 = -112.713192921 q = -112.713192921 Simplifying q = -112.713192921Solution
The solution to the problem is based on the solutions from the subproblems. q = {92.713192921, -112.713192921}
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