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Simplifying 0.5Q2 + -12Q + 8 = 0 Reorder the terms: 8 + -12Q + 0.5Q2 = 0 Solving 8 + -12Q + 0.5Q2 = 0 Solving for variable 'Q'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 16 + -24Q + Q2 = 0 Move the constant term to the right: Add '-16' to each side of the equation. 16 + -24Q + -16 + Q2 = 0 + -16 Reorder the terms: 16 + -16 + -24Q + Q2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -24Q + Q2 = 0 + -16 -24Q + Q2 = 0 + -16 Combine like terms: 0 + -16 = -16 -24Q + Q2 = -16 The Q term is -24Q. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24Q + 144 + Q2 = -16 + 144 Reorder the terms: 144 + -24Q + Q2 = -16 + 144 Combine like terms: -16 + 144 = 128 144 + -24Q + Q2 = 128 Factor a perfect square on the left side: (Q + -12)(Q + -12) = 128 Calculate the square root of the right side: 11.313708499 Break this problem into two subproblems by setting (Q + -12) equal to 11.313708499 and -11.313708499.Subproblem 1
Q + -12 = 11.313708499 Simplifying Q + -12 = 11.313708499 Reorder the terms: -12 + Q = 11.313708499 Solving -12 + Q = 11.313708499 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + Q = 11.313708499 + 12 Combine like terms: -12 + 12 = 0 0 + Q = 11.313708499 + 12 Q = 11.313708499 + 12 Combine like terms: 11.313708499 + 12 = 23.313708499 Q = 23.313708499 Simplifying Q = 23.313708499Subproblem 2
Q + -12 = -11.313708499 Simplifying Q + -12 = -11.313708499 Reorder the terms: -12 + Q = -11.313708499 Solving -12 + Q = -11.313708499 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + Q = -11.313708499 + 12 Combine like terms: -12 + 12 = 0 0 + Q = -11.313708499 + 12 Q = -11.313708499 + 12 Combine like terms: -11.313708499 + 12 = 0.686291501 Q = 0.686291501 Simplifying Q = 0.686291501Solution
The solution to the problem is based on the solutions from the subproblems. Q = {23.313708499, 0.686291501}
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