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Simplifying -0.002Q2 + 0.5Q = 10 Reorder the terms: 0.5Q + -0.002Q2 = 10 Solving 0.5Q + -0.002Q2 = 10 Solving for variable 'Q'. Reorder the terms: -10 + 0.5Q + -0.002Q2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 0.5Q + -0.002Q2 = 0 Begin completing the square. Divide all terms by -0.002 the coefficient of the squared term: Divide each side by '-0.002'. 5000 + -250Q + Q2 = 0 Move the constant term to the right: Add '-5000' to each side of the equation. 5000 + -250Q + -5000 + Q2 = 0 + -5000 Reorder the terms: 5000 + -5000 + -250Q + Q2 = 0 + -5000 Combine like terms: 5000 + -5000 = 0 0 + -250Q + Q2 = 0 + -5000 -250Q + Q2 = 0 + -5000 Combine like terms: 0 + -5000 = -5000 -250Q + Q2 = -5000 The Q term is -250Q. Take half its coefficient (-125). Square it (15625) and add it to both sides. Add '15625' to each side of the equation. -250Q + 15625 + Q2 = -5000 + 15625 Reorder the terms: 15625 + -250Q + Q2 = -5000 + 15625 Combine like terms: -5000 + 15625 = 10625 15625 + -250Q + Q2 = 10625 Factor a perfect square on the left side: (Q + -125)(Q + -125) = 10625 Calculate the square root of the right side: 103.07764064 Break this problem into two subproblems by setting (Q + -125) equal to 103.07764064 and -103.07764064.Subproblem 1
Q + -125 = 103.07764064 Simplifying Q + -125 = 103.07764064 Reorder the terms: -125 + Q = 103.07764064 Solving -125 + Q = 103.07764064 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + Q = 103.07764064 + 125 Combine like terms: -125 + 125 = 0 0 + Q = 103.07764064 + 125 Q = 103.07764064 + 125 Combine like terms: 103.07764064 + 125 = 228.07764064 Q = 228.07764064 Simplifying Q = 228.07764064Subproblem 2
Q + -125 = -103.07764064 Simplifying Q + -125 = -103.07764064 Reorder the terms: -125 + Q = -103.07764064 Solving -125 + Q = -103.07764064 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + Q = -103.07764064 + 125 Combine like terms: -125 + 125 = 0 0 + Q = -103.07764064 + 125 Q = -103.07764064 + 125 Combine like terms: -103.07764064 + 125 = 21.92235936 Q = 21.92235936 Simplifying Q = 21.92235936Solution
The solution to the problem is based on the solutions from the subproblems. Q = {228.07764064, 21.92235936}
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