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Simplifying 20625 = x(29 + -0.01x) 20625 = (29 * x + -0.01x * x) 20625 = (29x + -0.01x2) Solving 20625 = 29x + -0.01x2 Solving for variable 'x'. Reorder the terms: 20625 + -29x + 0.01x2 = 29x + -29x + -0.01x2 + 0.01x2 Combine like terms: 29x + -29x = 0 20625 + -29x + 0.01x2 = 0 + -0.01x2 + 0.01x2 20625 + -29x + 0.01x2 = -0.01x2 + 0.01x2 Combine like terms: -0.01x2 + 0.01x2 = 0.00 20625 + -29x + 0.01x2 = 0.00 Begin completing the square. Divide all terms by 0.01 the coefficient of the squared term: Divide each side by '0.01'. 2062500 + -2900x + x2 = 0 Move the constant term to the right: Add '-2062500' to each side of the equation. 2062500 + -2900x + -2062500 + x2 = 0 + -2062500 Reorder the terms: 2062500 + -2062500 + -2900x + x2 = 0 + -2062500 Combine like terms: 2062500 + -2062500 = 0 0 + -2900x + x2 = 0 + -2062500 -2900x + x2 = 0 + -2062500 Combine like terms: 0 + -2062500 = -2062500 -2900x + x2 = -2062500 The x term is -2900x. Take half its coefficient (-1450). Square it (2102500) and add it to both sides. Add '2102500' to each side of the equation. -2900x + 2102500 + x2 = -2062500 + 2102500 Reorder the terms: 2102500 + -2900x + x2 = -2062500 + 2102500 Combine like terms: -2062500 + 2102500 = 40000 2102500 + -2900x + x2 = 40000 Factor a perfect square on the left side: (x + -1450)(x + -1450) = 40000 Calculate the square root of the right side: 200 Break this problem into two subproblems by setting (x + -1450) equal to 200 and -200.Subproblem 1
x + -1450 = 200 Simplifying x + -1450 = 200 Reorder the terms: -1450 + x = 200 Solving -1450 + x = 200 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1450' to each side of the equation. -1450 + 1450 + x = 200 + 1450 Combine like terms: -1450 + 1450 = 0 0 + x = 200 + 1450 x = 200 + 1450 Combine like terms: 200 + 1450 = 1650 x = 1650 Simplifying x = 1650Subproblem 2
x + -1450 = -200 Simplifying x + -1450 = -200 Reorder the terms: -1450 + x = -200 Solving -1450 + x = -200 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1450' to each side of the equation. -1450 + 1450 + x = -200 + 1450 Combine like terms: -1450 + 1450 = 0 0 + x = -200 + 1450 x = -200 + 1450 Combine like terms: -200 + 1450 = 1250 x = 1250 Simplifying x = 1250Solution
The solution to the problem is based on the solutions from the subproblems. x = {1650, 1250}
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