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Simplifying 2000000x + 3x * x = 250000000 Multiply x * x 2000000x + 3x2 = 250000000 Solving 2000000x + 3x2 = 250000000 Solving for variable 'x'. Reorder the terms: -250000000 + 2000000x + 3x2 = 250000000 + -250000000 Combine like terms: 250000000 + -250000000 = 0 -250000000 + 2000000x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -83333333.33 + 666666.6667x + x2 = 0 Move the constant term to the right: Add '83333333.33' to each side of the equation. -83333333.33 + 666666.6667x + 83333333.33 + x2 = 0 + 83333333.33 Reorder the terms: -83333333.33 + 83333333.33 + 666666.6667x + x2 = 0 + 83333333.33 Combine like terms: -83333333.33 + 83333333.33 = 0.00 0.00 + 666666.6667x + x2 = 0 + 83333333.33 666666.6667x + x2 = 0 + 83333333.33 Combine like terms: 0 + 83333333.33 = 83333333.33 666666.6667x + x2 = 83333333.33 The x term is 666666.6667x. Take half its coefficient (333333.3334). Square it (111111111200) and add it to both sides. Add '111111111200' to each side of the equation. 666666.6667x + 111111111200 + x2 = 83333333.33 + 111111111200 Reorder the terms: 111111111200 + 666666.6667x + x2 = 83333333.33 + 111111111200 Combine like terms: 83333333.33 + 111111111200 = 111194444533.33 111111111200 + 666666.6667x + x2 = 111194444533.33 Factor a perfect square on the left side: (x + 333333.3334)(x + 333333.3334) = 111194444533.33 Calculate the square root of the right side: 333458.310037897 Break this problem into two subproblems by setting (x + 333333.3334) equal to 333458.310037897 and -333458.310037897.Subproblem 1
x + 333333.3334 = 333458.310037897 Simplifying x + 333333.3334 = 333458.310037897 Reorder the terms: 333333.3334 + x = 333458.310037897 Solving 333333.3334 + x = 333458.310037897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-333333.3334' to each side of the equation. 333333.3334 + -333333.3334 + x = 333458.310037897 + -333333.3334 Combine like terms: 333333.3334 + -333333.3334 = 0.0000 0.0000 + x = 333458.310037897 + -333333.3334 x = 333458.310037897 + -333333.3334 Combine like terms: 333458.310037897 + -333333.3334 = 124.976637897 x = 124.976637897 Simplifying x = 124.976637897Subproblem 2
x + 333333.3334 = -333458.310037897 Simplifying x + 333333.3334 = -333458.310037897 Reorder the terms: 333333.3334 + x = -333458.310037897 Solving 333333.3334 + x = -333458.310037897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-333333.3334' to each side of the equation. 333333.3334 + -333333.3334 + x = -333458.310037897 + -333333.3334 Combine like terms: 333333.3334 + -333333.3334 = 0.0000 0.0000 + x = -333458.310037897 + -333333.3334 x = -333458.310037897 + -333333.3334 Combine like terms: -333458.310037897 + -333333.3334 = -666791.643437897 x = -666791.643437897 Simplifying x = -666791.643437897Solution
The solution to the problem is based on the solutions from the subproblems. x = {124.976637897, -666791.643437897}
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