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Simplifying Q2 + -3Q = 3 Reorder the terms: -3Q + Q2 = 3 Solving -3Q + Q2 = 3 Solving for variable 'Q'. Reorder the terms: -3 + -3Q + Q2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -3Q + Q2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -3Q + 3 + Q2 = 0 + 3 Reorder the terms: -3 + 3 + -3Q + Q2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -3Q + Q2 = 0 + 3 -3Q + Q2 = 0 + 3 Combine like terms: 0 + 3 = 3 -3Q + Q2 = 3 The Q term is -3Q. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3Q + 2.25 + Q2 = 3 + 2.25 Reorder the terms: 2.25 + -3Q + Q2 = 3 + 2.25 Combine like terms: 3 + 2.25 = 5.25 2.25 + -3Q + Q2 = 5.25 Factor a perfect square on the left side: (Q + -1.5)(Q + -1.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (Q + -1.5) equal to 2.291287847 and -2.291287847.Subproblem 1
Q + -1.5 = 2.291287847 Simplifying Q + -1.5 = 2.291287847 Reorder the terms: -1.5 + Q = 2.291287847 Solving -1.5 + Q = 2.291287847 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + Q = 2.291287847 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + Q = 2.291287847 + 1.5 Q = 2.291287847 + 1.5 Combine like terms: 2.291287847 + 1.5 = 3.791287847 Q = 3.791287847 Simplifying Q = 3.791287847Subproblem 2
Q + -1.5 = -2.291287847 Simplifying Q + -1.5 = -2.291287847 Reorder the terms: -1.5 + Q = -2.291287847 Solving -1.5 + Q = -2.291287847 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + Q = -2.291287847 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + Q = -2.291287847 + 1.5 Q = -2.291287847 + 1.5 Combine like terms: -2.291287847 + 1.5 = -0.791287847 Q = -0.791287847 Simplifying Q = -0.791287847Solution
The solution to the problem is based on the solutions from the subproblems. Q = {3.791287847, -0.791287847}
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