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Simplifying -3Q2 + 12Q + 2 = 0 Reorder the terms: 2 + 12Q + -3Q2 = 0 Solving 2 + 12Q + -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'. -0.6666666667 + -4Q + Q2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -4Q + 0.6666666667 + Q2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -4Q + Q2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -4Q + Q2 = 0 + 0.6666666667 -4Q + Q2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -4Q + Q2 = 0.6666666667 The Q term is -4Q. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4Q + 4 + Q2 = 0.6666666667 + 4 Reorder the terms: 4 + -4Q + Q2 = 0.6666666667 + 4 Combine like terms: 0.6666666667 + 4 = 4.6666666667 4 + -4Q + Q2 = 4.6666666667 Factor a perfect square on the left side: (Q + -2)(Q + -2) = 4.6666666667 Calculate the square root of the right side: 2.160246899 Break this problem into two subproblems by setting (Q + -2) equal to 2.160246899 and -2.160246899.Subproblem 1
Q + -2 = 2.160246899 Simplifying Q + -2 = 2.160246899 Reorder the terms: -2 + Q = 2.160246899 Solving -2 + Q = 2.160246899 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + Q = 2.160246899 + 2 Combine like terms: -2 + 2 = 0 0 + Q = 2.160246899 + 2 Q = 2.160246899 + 2 Combine like terms: 2.160246899 + 2 = 4.160246899 Q = 4.160246899 Simplifying Q = 4.160246899Subproblem 2
Q + -2 = -2.160246899 Simplifying Q + -2 = -2.160246899 Reorder the terms: -2 + Q = -2.160246899 Solving -2 + Q = -2.160246899 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + Q = -2.160246899 + 2 Combine like terms: -2 + 2 = 0 0 + Q = -2.160246899 + 2 Q = -2.160246899 + 2 Combine like terms: -2.160246899 + 2 = -0.160246899 Q = -0.160246899 Simplifying Q = -0.160246899Solution
The solution to the problem is based on the solutions from the subproblems. Q = {4.160246899, -0.160246899}
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