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Simplifying 35x = -0.05x2 + 5000 Reorder the terms: 35x = 5000 + -0.05x2 Solving 35x = 5000 + -0.05x2 Solving for variable 'x'. Reorder the terms: -5000 + 35x + 0.05x2 = 5000 + -0.05x2 + -5000 + 0.05x2 Reorder the terms: -5000 + 35x + 0.05x2 = 5000 + -5000 + -0.05x2 + 0.05x2 Combine like terms: 5000 + -5000 = 0 -5000 + 35x + 0.05x2 = 0 + -0.05x2 + 0.05x2 -5000 + 35x + 0.05x2 = -0.05x2 + 0.05x2 Combine like terms: -0.05x2 + 0.05x2 = 0.00 -5000 + 35x + 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'. -100000 + 700x + x2 = 0 Move the constant term to the right: Add '100000' to each side of the equation. -100000 + 700x + 100000 + x2 = 0 + 100000 Reorder the terms: -100000 + 100000 + 700x + x2 = 0 + 100000 Combine like terms: -100000 + 100000 = 0 0 + 700x + x2 = 0 + 100000 700x + x2 = 0 + 100000 Combine like terms: 0 + 100000 = 100000 700x + x2 = 100000 The x term is 700x. Take half its coefficient (350). Square it (122500) and add it to both sides. Add '122500' to each side of the equation. 700x + 122500 + x2 = 100000 + 122500 Reorder the terms: 122500 + 700x + x2 = 100000 + 122500 Combine like terms: 100000 + 122500 = 222500 122500 + 700x + x2 = 222500 Factor a perfect square on the left side: (x + 350)(x + 350) = 222500 Calculate the square root of the right side: 471.699056603 Break this problem into two subproblems by setting (x + 350) equal to 471.699056603 and -471.699056603.Subproblem 1
x + 350 = 471.699056603 Simplifying x + 350 = 471.699056603 Reorder the terms: 350 + x = 471.699056603 Solving 350 + x = 471.699056603 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-350' to each side of the equation. 350 + -350 + x = 471.699056603 + -350 Combine like terms: 350 + -350 = 0 0 + x = 471.699056603 + -350 x = 471.699056603 + -350 Combine like terms: 471.699056603 + -350 = 121.699056603 x = 121.699056603 Simplifying x = 121.699056603Subproblem 2
x + 350 = -471.699056603 Simplifying x + 350 = -471.699056603 Reorder the terms: 350 + x = -471.699056603 Solving 350 + x = -471.699056603 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-350' to each side of the equation. 350 + -350 + x = -471.699056603 + -350 Combine like terms: 350 + -350 = 0 0 + x = -471.699056603 + -350 x = -471.699056603 + -350 Combine like terms: -471.699056603 + -350 = -821.699056603 x = -821.699056603 Simplifying x = -821.699056603Solution
The solution to the problem is based on the solutions from the subproblems. x = {121.699056603, -821.699056603}
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