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Simplifying 10000 + 10Q = 0.1Q2 Solving 10000 + 10Q = 0.1Q2 Solving for variable 'Q'. Combine like terms: 0.1Q2 + -0.1Q2 = 0.0 10000 + 10Q + -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'. -100000 + -100Q + Q2 = 0 Move the constant term to the right: Add '100000' to each side of the equation. -100000 + -100Q + 100000 + Q2 = 0 + 100000 Reorder the terms: -100000 + 100000 + -100Q + Q2 = 0 + 100000 Combine like terms: -100000 + 100000 = 0 0 + -100Q + Q2 = 0 + 100000 -100Q + Q2 = 0 + 100000 Combine like terms: 0 + 100000 = 100000 -100Q + Q2 = 100000 The Q term is -100Q. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100Q + 2500 + Q2 = 100000 + 2500 Reorder the terms: 2500 + -100Q + Q2 = 100000 + 2500 Combine like terms: 100000 + 2500 = 102500 2500 + -100Q + Q2 = 102500 Factor a perfect square on the left side: (Q + -50)(Q + -50) = 102500 Calculate the square root of the right side: 320.156211872 Break this problem into two subproblems by setting (Q + -50) equal to 320.156211872 and -320.156211872.Subproblem 1
Q + -50 = 320.156211872 Simplifying Q + -50 = 320.156211872 Reorder the terms: -50 + Q = 320.156211872 Solving -50 + Q = 320.156211872 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + Q = 320.156211872 + 50 Combine like terms: -50 + 50 = 0 0 + Q = 320.156211872 + 50 Q = 320.156211872 + 50 Combine like terms: 320.156211872 + 50 = 370.156211872 Q = 370.156211872 Simplifying Q = 370.156211872Subproblem 2
Q + -50 = -320.156211872 Simplifying Q + -50 = -320.156211872 Reorder the terms: -50 + Q = -320.156211872 Solving -50 + Q = -320.156211872 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + Q = -320.156211872 + 50 Combine like terms: -50 + 50 = 0 0 + Q = -320.156211872 + 50 Q = -320.156211872 + 50 Combine like terms: -320.156211872 + 50 = -270.156211872 Q = -270.156211872 Simplifying Q = -270.156211872Solution
The solution to the problem is based on the solutions from the subproblems. Q = {370.156211872, -270.156211872}
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