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Simplifying -24.999Q2 + 700Q + -2400 = 0 Reorder the terms: -2400 + 700Q + -24.999Q2 = 0 Solving -2400 + 700Q + -24.999Q2 = 0 Solving for variable 'Q'. Begin completing the square. Divide all terms by -24.999 the coefficient of the squared term: Divide each side by '-24.999'. 96.00384015 + -28.00112004Q + Q2 = 0 Move the constant term to the right: Add '-96.00384015' to each side of the equation. 96.00384015 + -28.00112004Q + -96.00384015 + Q2 = 0 + -96.00384015 Reorder the terms: 96.00384015 + -96.00384015 + -28.00112004Q + Q2 = 0 + -96.00384015 Combine like terms: 96.00384015 + -96.00384015 = 0.00000000 0.00000000 + -28.00112004Q + Q2 = 0 + -96.00384015 -28.00112004Q + Q2 = 0 + -96.00384015 Combine like terms: 0 + -96.00384015 = -96.00384015 -28.00112004Q + Q2 = -96.00384015 The Q term is -28.00112004Q. Take half its coefficient (-14.00056002). Square it (196.0156809) and add it to both sides. Add '196.0156809' to each side of the equation. -28.00112004Q + 196.0156809 + Q2 = -96.00384015 + 196.0156809 Reorder the terms: 196.0156809 + -28.00112004Q + Q2 = -96.00384015 + 196.0156809 Combine like terms: -96.00384015 + 196.0156809 = 100.01184075 196.0156809 + -28.00112004Q + Q2 = 100.01184075 Factor a perfect square on the left side: (Q + -14.00056002)(Q + -14.00056002) = 100.01184075 Calculate the square root of the right side: 10.00059202 Break this problem into two subproblems by setting (Q + -14.00056002) equal to 10.00059202 and -10.00059202.Subproblem 1
Q + -14.00056002 = 10.00059202 Simplifying Q + -14.00056002 = 10.00059202 Reorder the terms: -14.00056002 + Q = 10.00059202 Solving -14.00056002 + Q = 10.00059202 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '14.00056002' to each side of the equation. -14.00056002 + 14.00056002 + Q = 10.00059202 + 14.00056002 Combine like terms: -14.00056002 + 14.00056002 = 0.00000000 0.00000000 + Q = 10.00059202 + 14.00056002 Q = 10.00059202 + 14.00056002 Combine like terms: 10.00059202 + 14.00056002 = 24.00115204 Q = 24.00115204 Simplifying Q = 24.00115204Subproblem 2
Q + -14.00056002 = -10.00059202 Simplifying Q + -14.00056002 = -10.00059202 Reorder the terms: -14.00056002 + Q = -10.00059202 Solving -14.00056002 + Q = -10.00059202 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '14.00056002' to each side of the equation. -14.00056002 + 14.00056002 + Q = -10.00059202 + 14.00056002 Combine like terms: -14.00056002 + 14.00056002 = 0.00000000 0.00000000 + Q = -10.00059202 + 14.00056002 Q = -10.00059202 + 14.00056002 Combine like terms: -10.00059202 + 14.00056002 = 3.999968 Q = 3.999968 Simplifying Q = 3.999968Solution
The solution to the problem is based on the solutions from the subproblems. Q = {24.00115204, 3.999968}
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