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Simplifying 5x + 12x(x + 5000) = 940 Reorder the terms: 5x + 12x(5000 + x) = 940 5x + (5000 * 12x + x * 12x) = 940 5x + (60000x + 12x2) = 940 Combine like terms: 5x + 60000x = 60005x 60005x + 12x2 = 940 Solving 60005x + 12x2 = 940 Solving for variable 'x'. Reorder the terms: -940 + 60005x + 12x2 = 940 + -940 Combine like terms: 940 + -940 = 0 -940 + 60005x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -78.33333333 + 5000.416667x + x2 = 0 Move the constant term to the right: Add '78.33333333' to each side of the equation. -78.33333333 + 5000.416667x + 78.33333333 + x2 = 0 + 78.33333333 Reorder the terms: -78.33333333 + 78.33333333 + 5000.416667x + x2 = 0 + 78.33333333 Combine like terms: -78.33333333 + 78.33333333 = 0.00000000 0.00000000 + 5000.416667x + x2 = 0 + 78.33333333 5000.416667x + x2 = 0 + 78.33333333 Combine like terms: 0 + 78.33333333 = 78.33333333 5000.416667x + x2 = 78.33333333 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 = 78.33333333 + 6251041.713 Reorder the terms: 6251041.713 + 5000.416667x + x2 = 78.33333333 + 6251041.713 Combine like terms: 78.33333333 + 6251041.713 = 6251120.04633333 6251041.713 + 5000.416667x + x2 = 6251120.04633333 Factor a perfect square on the left side: (x + 2500.208334)(x + 2500.208334) = 6251120.04633333 Calculate the square root of the right side: 2500.223999232 Break this problem into two subproblems by setting (x + 2500.208334) equal to 2500.223999232 and -2500.223999232.Subproblem 1
x + 2500.208334 = 2500.223999232 Simplifying x + 2500.208334 = 2500.223999232 Reorder the terms: 2500.208334 + x = 2500.223999232 Solving 2500.208334 + x = 2500.223999232 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 = 2500.223999232 + -2500.208334 Combine like terms: 2500.208334 + -2500.208334 = 0.000000 0.000000 + x = 2500.223999232 + -2500.208334 x = 2500.223999232 + -2500.208334 Combine like terms: 2500.223999232 + -2500.208334 = 0.015665232 x = 0.015665232 Simplifying x = 0.015665232Subproblem 2
x + 2500.208334 = -2500.223999232 Simplifying x + 2500.208334 = -2500.223999232 Reorder the terms: 2500.208334 + x = -2500.223999232 Solving 2500.208334 + x = -2500.223999232 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 = -2500.223999232 + -2500.208334 Combine like terms: 2500.208334 + -2500.208334 = 0.000000 0.000000 + x = -2500.223999232 + -2500.208334 x = -2500.223999232 + -2500.208334 Combine like terms: -2500.223999232 + -2500.208334 = -5000.432333232 x = -5000.432333232 Simplifying x = -5000.432333232Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.015665232, -5000.432333232}
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