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Simplifying 730Q + -24Q2 + -225 = 0 Reorder the terms: -225 + 730Q + -24Q2 = 0 Solving -225 + 730Q + -24Q2 = 0 Solving for variable 'Q'. Begin completing the square. Divide all terms by -24 the coefficient of the squared term: Divide each side by '-24'. 9.375 + -30.41666667Q + Q2 = 0 Move the constant term to the right: Add '-9.375' to each side of the equation. 9.375 + -30.41666667Q + -9.375 + Q2 = 0 + -9.375 Reorder the terms: 9.375 + -9.375 + -30.41666667Q + Q2 = 0 + -9.375 Combine like terms: 9.375 + -9.375 = 0.000 0.000 + -30.41666667Q + Q2 = 0 + -9.375 -30.41666667Q + Q2 = 0 + -9.375 Combine like terms: 0 + -9.375 = -9.375 -30.41666667Q + Q2 = -9.375 The Q term is -30.41666667Q. Take half its coefficient (-15.20833334). Square it (231.2934030) and add it to both sides. Add '231.2934030' to each side of the equation. -30.41666667Q + 231.2934030 + Q2 = -9.375 + 231.2934030 Reorder the terms: 231.2934030 + -30.41666667Q + Q2 = -9.375 + 231.2934030 Combine like terms: -9.375 + 231.2934030 = 221.918403 231.2934030 + -30.41666667Q + Q2 = 221.918403 Factor a perfect square on the left side: (Q + -15.20833334)(Q + -15.20833334) = 221.918403 Calculate the square root of the right side: 14.896925958 Break this problem into two subproblems by setting (Q + -15.20833334) equal to 14.896925958 and -14.896925958.Subproblem 1
Q + -15.20833334 = 14.896925958 Simplifying Q + -15.20833334 = 14.896925958 Reorder the terms: -15.20833334 + Q = 14.896925958 Solving -15.20833334 + Q = 14.896925958 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '15.20833334' to each side of the equation. -15.20833334 + 15.20833334 + Q = 14.896925958 + 15.20833334 Combine like terms: -15.20833334 + 15.20833334 = 0.00000000 0.00000000 + Q = 14.896925958 + 15.20833334 Q = 14.896925958 + 15.20833334 Combine like terms: 14.896925958 + 15.20833334 = 30.105259298 Q = 30.105259298 Simplifying Q = 30.105259298Subproblem 2
Q + -15.20833334 = -14.896925958 Simplifying Q + -15.20833334 = -14.896925958 Reorder the terms: -15.20833334 + Q = -14.896925958 Solving -15.20833334 + Q = -14.896925958 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '15.20833334' to each side of the equation. -15.20833334 + 15.20833334 + Q = -14.896925958 + 15.20833334 Combine like terms: -15.20833334 + 15.20833334 = 0.00000000 0.00000000 + Q = -14.896925958 + 15.20833334 Q = -14.896925958 + 15.20833334 Combine like terms: -14.896925958 + 15.20833334 = 0.311407382 Q = 0.311407382 Simplifying Q = 0.311407382Solution
The solution to the problem is based on the solutions from the subproblems. Q = {30.105259298, 0.311407382}
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