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Simplifying 50 = 82.144177 + -0.829392Q + 0.0021324Q2 Solving 50 = 82.144177 + -0.829392Q + 0.0021324Q2 Solving for variable 'Q'. Combine like terms: 50 + -82.144177 = -32.144177 -32.144177 + 0.829392Q + -0.0021324Q2 = 82.144177 + -0.829392Q + 0.0021324Q2 + -82.144177 + 0.829392Q + -0.0021324Q2 Reorder the terms: -32.144177 + 0.829392Q + -0.0021324Q2 = 82.144177 + -82.144177 + -0.829392Q + 0.829392Q + 0.0021324Q2 + -0.0021324Q2 Combine like terms: 82.144177 + -82.144177 = 0.000000 -32.144177 + 0.829392Q + -0.0021324Q2 = 0.000000 + -0.829392Q + 0.829392Q + 0.0021324Q2 + -0.0021324Q2 -32.144177 + 0.829392Q + -0.0021324Q2 = -0.829392Q + 0.829392Q + 0.0021324Q2 + -0.0021324Q2 Combine like terms: -0.829392Q + 0.829392Q = 0.000000 -32.144177 + 0.829392Q + -0.0021324Q2 = 0.000000 + 0.0021324Q2 + -0.0021324Q2 -32.144177 + 0.829392Q + -0.0021324Q2 = 0.0021324Q2 + -0.0021324Q2 Combine like terms: 0.0021324Q2 + -0.0021324Q2 = 0.0000000 -32.144177 + 0.829392Q + -0.0021324Q2 = 0.0000000 Begin completing the square. Divide all terms by -0.0021324 the coefficient of the squared term: Divide each side by '-0.0021324'. 15074.17792 + -388.9476646Q + Q2 = 0 Move the constant term to the right: Add '-15074.17792' to each side of the equation. 15074.17792 + -388.9476646Q + -15074.17792 + Q2 = 0 + -15074.17792 Reorder the terms: 15074.17792 + -15074.17792 + -388.9476646Q + Q2 = 0 + -15074.17792 Combine like terms: 15074.17792 + -15074.17792 = 0.00000 0.00000 + -388.9476646Q + Q2 = 0 + -15074.17792 -388.9476646Q + Q2 = 0 + -15074.17792 Combine like terms: 0 + -15074.17792 = -15074.17792 -388.9476646Q + Q2 = -15074.17792 The Q term is -388.9476646Q. Take half its coefficient (-194.4738323). Square it (37820.07145) and add it to both sides. Add '37820.07145' to each side of the equation. -388.9476646Q + 37820.07145 + Q2 = -15074.17792 + 37820.07145 Reorder the terms: 37820.07145 + -388.9476646Q + Q2 = -15074.17792 + 37820.07145 Combine like terms: -15074.17792 + 37820.07145 = 22745.89353 37820.07145 + -388.9476646Q + Q2 = 22745.89353 Factor a perfect square on the left side: (Q + -194.4738323)(Q + -194.4738323) = 22745.89353 Calculate the square root of the right side: 150.81741786 Break this problem into two subproblems by setting (Q + -194.4738323) equal to 150.81741786 and -150.81741786.Subproblem 1
Q + -194.4738323 = 150.81741786 Simplifying Q + -194.4738323 = 150.81741786 Reorder the terms: -194.4738323 + Q = 150.81741786 Solving -194.4738323 + Q = 150.81741786 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '194.4738323' to each side of the equation. -194.4738323 + 194.4738323 + Q = 150.81741786 + 194.4738323 Combine like terms: -194.4738323 + 194.4738323 = 0.0000000 0.0000000 + Q = 150.81741786 + 194.4738323 Q = 150.81741786 + 194.4738323 Combine like terms: 150.81741786 + 194.4738323 = 345.29125016 Q = 345.29125016 Simplifying Q = 345.29125016Subproblem 2
Q + -194.4738323 = -150.81741786 Simplifying Q + -194.4738323 = -150.81741786 Reorder the terms: -194.4738323 + Q = -150.81741786 Solving -194.4738323 + Q = -150.81741786 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '194.4738323' to each side of the equation. -194.4738323 + 194.4738323 + Q = -150.81741786 + 194.4738323 Combine like terms: -194.4738323 + 194.4738323 = 0.0000000 0.0000000 + Q = -150.81741786 + 194.4738323 Q = -150.81741786 + 194.4738323 Combine like terms: -150.81741786 + 194.4738323 = 43.65641444 Q = 43.65641444 Simplifying Q = 43.65641444Solution
The solution to the problem is based on the solutions from the subproblems. Q = {345.29125016, 43.65641444}
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