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Simplifying 60 = x(5 + -0.05x) 60 = (5 * x + -0.05x * x) 60 = (5x + -0.05x2) Solving 60 = 5x + -0.05x2 Solving for variable 'x'. Reorder the terms: 60 + -5x + 0.05x2 = 5x + -5x + -0.05x2 + 0.05x2 Combine like terms: 5x + -5x = 0 60 + -5x + 0.05x2 = 0 + -0.05x2 + 0.05x2 60 + -5x + 0.05x2 = -0.05x2 + 0.05x2 Combine like terms: -0.05x2 + 0.05x2 = 0.00 60 + -5x + 0.05x2 = 0.00 Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. 1200 + -100x + x2 = 0 Move the constant term to the right: Add '-1200' to each side of the equation. 1200 + -100x + -1200 + x2 = 0 + -1200 Reorder the terms: 1200 + -1200 + -100x + x2 = 0 + -1200 Combine like terms: 1200 + -1200 = 0 0 + -100x + x2 = 0 + -1200 -100x + x2 = 0 + -1200 Combine like terms: 0 + -1200 = -1200 -100x + x2 = -1200 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = -1200 + 2500 Reorder the terms: 2500 + -100x + x2 = -1200 + 2500 Combine like terms: -1200 + 2500 = 1300 2500 + -100x + x2 = 1300 Factor a perfect square on the left side: (x + -50)(x + -50) = 1300 Calculate the square root of the right side: 36.055512755 Break this problem into two subproblems by setting (x + -50) equal to 36.055512755 and -36.055512755.Subproblem 1
x + -50 = 36.055512755 Simplifying x + -50 = 36.055512755 Reorder the terms: -50 + x = 36.055512755 Solving -50 + x = 36.055512755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 36.055512755 + 50 Combine like terms: -50 + 50 = 0 0 + x = 36.055512755 + 50 x = 36.055512755 + 50 Combine like terms: 36.055512755 + 50 = 86.055512755 x = 86.055512755 Simplifying x = 86.055512755Subproblem 2
x + -50 = -36.055512755 Simplifying x + -50 = -36.055512755 Reorder the terms: -50 + x = -36.055512755 Solving -50 + x = -36.055512755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -36.055512755 + 50 Combine like terms: -50 + 50 = 0 0 + x = -36.055512755 + 50 x = -36.055512755 + 50 Combine like terms: -36.055512755 + 50 = 13.944487245 x = 13.944487245 Simplifying x = 13.944487245Solution
The solution to the problem is based on the solutions from the subproblems. x = {86.055512755, 13.944487245}
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