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Simplifying Q2 + -20Q + 80 = 0 Reorder the terms: 80 + -20Q + Q2 = 0 Solving 80 + -20Q + Q2 = 0 Solving for variable 'Q'. Begin completing the square. Move the constant term to the right: Add '-80' to each side of the equation. 80 + -20Q + -80 + Q2 = 0 + -80 Reorder the terms: 80 + -80 + -20Q + Q2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + -20Q + Q2 = 0 + -80 -20Q + Q2 = 0 + -80 Combine like terms: 0 + -80 = -80 -20Q + Q2 = -80 The Q term is -20Q. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20Q + 100 + Q2 = -80 + 100 Reorder the terms: 100 + -20Q + Q2 = -80 + 100 Combine like terms: -80 + 100 = 20 100 + -20Q + Q2 = 20 Factor a perfect square on the left side: (Q + -10)(Q + -10) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (Q + -10) equal to 4.472135955 and -4.472135955.Subproblem 1
Q + -10 = 4.472135955 Simplifying Q + -10 = 4.472135955 Reorder the terms: -10 + Q = 4.472135955 Solving -10 + Q = 4.472135955 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + Q = 4.472135955 + 10 Combine like terms: -10 + 10 = 0 0 + Q = 4.472135955 + 10 Q = 4.472135955 + 10 Combine like terms: 4.472135955 + 10 = 14.472135955 Q = 14.472135955 Simplifying Q = 14.472135955Subproblem 2
Q + -10 = -4.472135955 Simplifying Q + -10 = -4.472135955 Reorder the terms: -10 + Q = -4.472135955 Solving -10 + Q = -4.472135955 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + Q = -4.472135955 + 10 Combine like terms: -10 + 10 = 0 0 + Q = -4.472135955 + 10 Q = -4.472135955 + 10 Combine like terms: -4.472135955 + 10 = 5.527864045 Q = 5.527864045 Simplifying Q = 5.527864045Solution
The solution to the problem is based on the solutions from the subproblems. Q = {14.472135955, 5.527864045}
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