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Simplifying 0.1q2 + q = 0.2q + 1 Reorder the terms: q + 0.1q2 = 0.2q + 1 Reorder the terms: q + 0.1q2 = 1 + 0.2q Solving q + 0.1q2 = 1 + 0.2q Solving for variable 'q'. Reorder the terms: -1 + q + -0.2q + 0.1q2 = 1 + 0.2q + -1 + -0.2q Combine like terms: q + -0.2q = 0.8q -1 + 0.8q + 0.1q2 = 1 + 0.2q + -1 + -0.2q Reorder the terms: -1 + 0.8q + 0.1q2 = 1 + -1 + 0.2q + -0.2q Combine like terms: 1 + -1 = 0 -1 + 0.8q + 0.1q2 = 0 + 0.2q + -0.2q -1 + 0.8q + 0.1q2 = 0.2q + -0.2q Combine like terms: 0.2q + -0.2q = 0.0 -1 + 0.8q + 0.1q2 = 0.0 Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. -10 + 8q + q2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 8q + 10 + q2 = 0 + 10 Reorder the terms: -10 + 10 + 8q + q2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 8q + q2 = 0 + 10 8q + q2 = 0 + 10 Combine like terms: 0 + 10 = 10 8q + q2 = 10 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 = 10 + 16 Reorder the terms: 16 + 8q + q2 = 10 + 16 Combine like terms: 10 + 16 = 26 16 + 8q + q2 = 26 Factor a perfect square on the left side: (q + 4)(q + 4) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (q + 4) equal to 5.099019514 and -5.099019514.Subproblem 1
q + 4 = 5.099019514 Simplifying q + 4 = 5.099019514 Reorder the terms: 4 + q = 5.099019514 Solving 4 + q = 5.099019514 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 = 5.099019514 + -4 Combine like terms: 4 + -4 = 0 0 + q = 5.099019514 + -4 q = 5.099019514 + -4 Combine like terms: 5.099019514 + -4 = 1.099019514 q = 1.099019514 Simplifying q = 1.099019514Subproblem 2
q + 4 = -5.099019514 Simplifying q + 4 = -5.099019514 Reorder the terms: 4 + q = -5.099019514 Solving 4 + q = -5.099019514 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 = -5.099019514 + -4 Combine like terms: 4 + -4 = 0 0 + q = -5.099019514 + -4 q = -5.099019514 + -4 Combine like terms: -5.099019514 + -4 = -9.099019514 q = -9.099019514 Simplifying q = -9.099019514Solution
The solution to the problem is based on the solutions from the subproblems. q = {1.099019514, -9.099019514}
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