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Simplifying 50q2 + q = 120 Reorder the terms: q + 50q2 = 120 Solving q + 50q2 = 120 Solving for variable 'q'. Reorder the terms: -120 + q + 50q2 = 120 + -120 Combine like terms: 120 + -120 = 0 -120 + q + 50q2 = 0 Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. -2.4 + 0.02q + q2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + 0.02q + 2.4 + q2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + 0.02q + q2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + 0.02q + q2 = 0 + 2.4 0.02q + q2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 0.02q + q2 = 2.4 The q term is q. 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. 0.02q + 0.25 + q2 = 2.4 + 0.25 Reorder the terms: 0.25 + 0.02q + q2 = 2.4 + 0.25 Combine like terms: 2.4 + 0.25 = 2.65 0.25 + 0.02q + q2 = 2.65 Factor a perfect square on the left side: (q + 0.5)(q + 0.5) = 2.65 Calculate the square root of the right side: 1.62788206 Break this problem into two subproblems by setting (q + 0.5) equal to 1.62788206 and -1.62788206.Subproblem 1
q + 0.5 = 1.62788206 Simplifying q + 0.5 = 1.62788206 Reorder the terms: 0.5 + q = 1.62788206 Solving 0.5 + q = 1.62788206 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 = 1.62788206 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + q = 1.62788206 + -0.5 q = 1.62788206 + -0.5 Combine like terms: 1.62788206 + -0.5 = 1.12788206 q = 1.12788206 Simplifying q = 1.12788206Subproblem 2
q + 0.5 = -1.62788206 Simplifying q + 0.5 = -1.62788206 Reorder the terms: 0.5 + q = -1.62788206 Solving 0.5 + q = -1.62788206 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 = -1.62788206 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + q = -1.62788206 + -0.5 q = -1.62788206 + -0.5 Combine like terms: -1.62788206 + -0.5 = -2.12788206 q = -2.12788206 Simplifying q = -2.12788206Solution
The solution to the problem is based on the solutions from the subproblems. q = {1.12788206, -2.12788206}
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