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Simplifying 480 = x(50 + -0.2x) 480 = (50 * x + -0.2x * x) 480 = (50x + -0.2x2) Solving 480 = 50x + -0.2x2 Solving for variable 'x'. Reorder the terms: 480 + -50x + 0.2x2 = 50x + -50x + -0.2x2 + 0.2x2 Combine like terms: 50x + -50x = 0 480 + -50x + 0.2x2 = 0 + -0.2x2 + 0.2x2 480 + -50x + 0.2x2 = -0.2x2 + 0.2x2 Combine like terms: -0.2x2 + 0.2x2 = 0.0 480 + -50x + 0.2x2 = 0.0 Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. 2400 + -250x + x2 = 0 Move the constant term to the right: Add '-2400' to each side of the equation. 2400 + -250x + -2400 + x2 = 0 + -2400 Reorder the terms: 2400 + -2400 + -250x + x2 = 0 + -2400 Combine like terms: 2400 + -2400 = 0 0 + -250x + x2 = 0 + -2400 -250x + x2 = 0 + -2400 Combine like terms: 0 + -2400 = -2400 -250x + x2 = -2400 The x term is -250x. Take half its coefficient (-125). Square it (15625) and add it to both sides. Add '15625' to each side of the equation. -250x + 15625 + x2 = -2400 + 15625 Reorder the terms: 15625 + -250x + x2 = -2400 + 15625 Combine like terms: -2400 + 15625 = 13225 15625 + -250x + x2 = 13225 Factor a perfect square on the left side: (x + -125)(x + -125) = 13225 Calculate the square root of the right side: 115 Break this problem into two subproblems by setting (x + -125) equal to 115 and -115.Subproblem 1
x + -125 = 115 Simplifying x + -125 = 115 Reorder the terms: -125 + x = 115 Solving -125 + x = 115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + x = 115 + 125 Combine like terms: -125 + 125 = 0 0 + x = 115 + 125 x = 115 + 125 Combine like terms: 115 + 125 = 240 x = 240 Simplifying x = 240Subproblem 2
x + -125 = -115 Simplifying x + -125 = -115 Reorder the terms: -125 + x = -115 Solving -125 + x = -115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + x = -115 + 125 Combine like terms: -125 + 125 = 0 0 + x = -115 + 125 x = -115 + 125 Combine like terms: -115 + 125 = 10 x = 10 Simplifying x = 10Solution
The solution to the problem is based on the solutions from the subproblems. x = {240, 10}
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