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Simplifying 3Q2 + -118.5Q + 328.5 = 0 Reorder the terms: 328.5 + -118.5Q + 3Q2 = 0 Solving 328.5 + -118.5Q + 3Q2 = 0 Solving for variable 'Q'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 109.5 + -39.5Q + Q2 = 0 Move the constant term to the right: Add '-109.5' to each side of the equation. 109.5 + -39.5Q + -109.5 + Q2 = 0 + -109.5 Reorder the terms: 109.5 + -109.5 + -39.5Q + Q2 = 0 + -109.5 Combine like terms: 109.5 + -109.5 = 0.0 0.0 + -39.5Q + Q2 = 0 + -109.5 -39.5Q + Q2 = 0 + -109.5 Combine like terms: 0 + -109.5 = -109.5 -39.5Q + Q2 = -109.5 The Q term is -39.5Q. Take half its coefficient (-19.75). Square it (390.0625) and add it to both sides. Add '390.0625' to each side of the equation. -39.5Q + 390.0625 + Q2 = -109.5 + 390.0625 Reorder the terms: 390.0625 + -39.5Q + Q2 = -109.5 + 390.0625 Combine like terms: -109.5 + 390.0625 = 280.5625 390.0625 + -39.5Q + Q2 = 280.5625 Factor a perfect square on the left side: (Q + -19.75)(Q + -19.75) = 280.5625 Calculate the square root of the right side: 16.75 Break this problem into two subproblems by setting (Q + -19.75) equal to 16.75 and -16.75.Subproblem 1
Q + -19.75 = 16.75 Simplifying Q + -19.75 = 16.75 Reorder the terms: -19.75 + Q = 16.75 Solving -19.75 + Q = 16.75 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '19.75' to each side of the equation. -19.75 + 19.75 + Q = 16.75 + 19.75 Combine like terms: -19.75 + 19.75 = 0.00 0.00 + Q = 16.75 + 19.75 Q = 16.75 + 19.75 Combine like terms: 16.75 + 19.75 = 36.5 Q = 36.5 Simplifying Q = 36.5Subproblem 2
Q + -19.75 = -16.75 Simplifying Q + -19.75 = -16.75 Reorder the terms: -19.75 + Q = -16.75 Solving -19.75 + Q = -16.75 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '19.75' to each side of the equation. -19.75 + 19.75 + Q = -16.75 + 19.75 Combine like terms: -19.75 + 19.75 = 0.00 0.00 + Q = -16.75 + 19.75 Q = -16.75 + 19.75 Combine like terms: -16.75 + 19.75 = 3 Q = 3 Simplifying Q = 3Solution
The solution to the problem is based on the solutions from the subproblems. Q = {36.5, 3}
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