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Simplifying 25Q2 = 2Q + 1 Reorder the terms: 25Q2 = 1 + 2Q Solving 25Q2 = 1 + 2Q Solving for variable 'Q'. Reorder the terms: -1 + -2Q + 25Q2 = 1 + 2Q + -1 + -2Q Reorder the terms: -1 + -2Q + 25Q2 = 1 + -1 + 2Q + -2Q Combine like terms: 1 + -1 = 0 -1 + -2Q + 25Q2 = 0 + 2Q + -2Q -1 + -2Q + 25Q2 = 2Q + -2Q Combine like terms: 2Q + -2Q = 0 -1 + -2Q + 25Q2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.04 + -0.08Q + Q2 = 0 Move the constant term to the right: Add '0.04' to each side of the equation. -0.04 + -0.08Q + 0.04 + Q2 = 0 + 0.04 Reorder the terms: -0.04 + 0.04 + -0.08Q + Q2 = 0 + 0.04 Combine like terms: -0.04 + 0.04 = 0.00 0.00 + -0.08Q + Q2 = 0 + 0.04 -0.08Q + Q2 = 0 + 0.04 Combine like terms: 0 + 0.04 = 0.04 -0.08Q + Q2 = 0.04 The Q term is -0.08Q. Take half its coefficient (-0.04). Square it (0.0016) and add it to both sides. Add '0.0016' to each side of the equation. -0.08Q + 0.0016 + Q2 = 0.04 + 0.0016 Reorder the terms: 0.0016 + -0.08Q + Q2 = 0.04 + 0.0016 Combine like terms: 0.04 + 0.0016 = 0.0416 0.0016 + -0.08Q + Q2 = 0.0416 Factor a perfect square on the left side: (Q + -0.04)(Q + -0.04) = 0.0416 Calculate the square root of the right side: 0.203960781 Break this problem into two subproblems by setting (Q + -0.04) equal to 0.203960781 and -0.203960781.Subproblem 1
Q + -0.04 = 0.203960781 Simplifying Q + -0.04 = 0.203960781 Reorder the terms: -0.04 + Q = 0.203960781 Solving -0.04 + Q = 0.203960781 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '0.04' to each side of the equation. -0.04 + 0.04 + Q = 0.203960781 + 0.04 Combine like terms: -0.04 + 0.04 = 0.00 0.00 + Q = 0.203960781 + 0.04 Q = 0.203960781 + 0.04 Combine like terms: 0.203960781 + 0.04 = 0.243960781 Q = 0.243960781 Simplifying Q = 0.243960781Subproblem 2
Q + -0.04 = -0.203960781 Simplifying Q + -0.04 = -0.203960781 Reorder the terms: -0.04 + Q = -0.203960781 Solving -0.04 + Q = -0.203960781 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '0.04' to each side of the equation. -0.04 + 0.04 + Q = -0.203960781 + 0.04 Combine like terms: -0.04 + 0.04 = 0.00 0.00 + Q = -0.203960781 + 0.04 Q = -0.203960781 + 0.04 Combine like terms: -0.203960781 + 0.04 = -0.163960781 Q = -0.163960781 Simplifying Q = -0.163960781Solution
The solution to the problem is based on the solutions from the subproblems. Q = {0.243960781, -0.163960781}
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