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Simplifying -0.2Q2 + 112Q + -4160 = 0 Reorder the terms: -4160 + 112Q + -0.2Q2 = 0 Solving -4160 + 112Q + -0.2Q2 = 0 Solving for variable 'Q'. Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. 20800 + -560Q + Q2 = 0 Move the constant term to the right: Add '-20800' to each side of the equation. 20800 + -560Q + -20800 + Q2 = 0 + -20800 Reorder the terms: 20800 + -20800 + -560Q + Q2 = 0 + -20800 Combine like terms: 20800 + -20800 = 0 0 + -560Q + Q2 = 0 + -20800 -560Q + Q2 = 0 + -20800 Combine like terms: 0 + -20800 = -20800 -560Q + Q2 = -20800 The Q term is -560Q. Take half its coefficient (-280). Square it (78400) and add it to both sides. Add '78400' to each side of the equation. -560Q + 78400 + Q2 = -20800 + 78400 Reorder the terms: 78400 + -560Q + Q2 = -20800 + 78400 Combine like terms: -20800 + 78400 = 57600 78400 + -560Q + Q2 = 57600 Factor a perfect square on the left side: (Q + -280)(Q + -280) = 57600 Calculate the square root of the right side: 240 Break this problem into two subproblems by setting (Q + -280) equal to 240 and -240.Subproblem 1
Q + -280 = 240 Simplifying Q + -280 = 240 Reorder the terms: -280 + Q = 240 Solving -280 + Q = 240 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '280' to each side of the equation. -280 + 280 + Q = 240 + 280 Combine like terms: -280 + 280 = 0 0 + Q = 240 + 280 Q = 240 + 280 Combine like terms: 240 + 280 = 520 Q = 520 Simplifying Q = 520Subproblem 2
Q + -280 = -240 Simplifying Q + -280 = -240 Reorder the terms: -280 + Q = -240 Solving -280 + Q = -240 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '280' to each side of the equation. -280 + 280 + Q = -240 + 280 Combine like terms: -280 + 280 = 0 0 + Q = -240 + 280 Q = -240 + 280 Combine like terms: -240 + 280 = 40 Q = 40 Simplifying Q = 40Solution
The solution to the problem is based on the solutions from the subproblems. Q = {520, 40}
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