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Simplifying 0.05x + 0.12x(x + 5000) = 940 Reorder the terms: 0.05x + 0.12x(5000 + x) = 940 0.05x + (5000 * 0.12x + x * 0.12x) = 940 0.05x + (600x + 0.12x2) = 940 Combine like terms: 0.05x + 600x = 600.05x 600.05x + 0.12x2 = 940 Solving 600.05x + 0.12x2 = 940 Solving for variable 'x'. Reorder the terms: -940 + 600.05x + 0.12x2 = 940 + -940 Combine like terms: 940 + -940 = 0 -940 + 600.05x + 0.12x2 = 0 Begin completing the square. Divide all terms by 0.12 the coefficient of the squared term: Divide each side by '0.12'. -7833.333333 + 5000.416667x + x2 = 0 Move the constant term to the right: Add '7833.333333' to each side of the equation. -7833.333333 + 5000.416667x + 7833.333333 + x2 = 0 + 7833.333333 Reorder the terms: -7833.333333 + 7833.333333 + 5000.416667x + x2 = 0 + 7833.333333 Combine like terms: -7833.333333 + 7833.333333 = 0.000000 0.000000 + 5000.416667x + x2 = 0 + 7833.333333 5000.416667x + x2 = 0 + 7833.333333 Combine like terms: 0 + 7833.333333 = 7833.333333 5000.416667x + x2 = 7833.333333 The x term is 5000.416667x. Take half its coefficient (2500.208334). Square it (6251041.713) and add it to both sides. Add '6251041.713' to each side of the equation. 5000.416667x + 6251041.713 + x2 = 7833.333333 + 6251041.713 Reorder the terms: 6251041.713 + 5000.416667x + x2 = 7833.333333 + 6251041.713 Combine like terms: 7833.333333 + 6251041.713 = 6258875.046333 6251041.713 + 5000.416667x + x2 = 6258875.046333 Factor a perfect square on the left side: (x + 2500.208334)(x + 2500.208334) = 6258875.046333 Calculate the square root of the right side: 2501.774379582 Break this problem into two subproblems by setting (x + 2500.208334) equal to 2501.774379582 and -2501.774379582.Subproblem 1
x + 2500.208334 = 2501.774379582 Simplifying x + 2500.208334 = 2501.774379582 Reorder the terms: 2500.208334 + x = 2501.774379582 Solving 2500.208334 + x = 2501.774379582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2500.208334' to each side of the equation. 2500.208334 + -2500.208334 + x = 2501.774379582 + -2500.208334 Combine like terms: 2500.208334 + -2500.208334 = 0.000000 0.000000 + x = 2501.774379582 + -2500.208334 x = 2501.774379582 + -2500.208334 Combine like terms: 2501.774379582 + -2500.208334 = 1.566045582 x = 1.566045582 Simplifying x = 1.566045582Subproblem 2
x + 2500.208334 = -2501.774379582 Simplifying x + 2500.208334 = -2501.774379582 Reorder the terms: 2500.208334 + x = -2501.774379582 Solving 2500.208334 + x = -2501.774379582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2500.208334' to each side of the equation. 2500.208334 + -2500.208334 + x = -2501.774379582 + -2500.208334 Combine like terms: 2500.208334 + -2500.208334 = 0.000000 0.000000 + x = -2501.774379582 + -2500.208334 x = -2501.774379582 + -2500.208334 Combine like terms: -2501.774379582 + -2500.208334 = -5001.982713582 x = -5001.982713582 Simplifying x = -5001.982713582Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.566045582, -5001.982713582}
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