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Simplifying x = -3x2 + 8700x + -4857500 Reorder the terms: x = -4857500 + 8700x + -3x2 Solving x = -4857500 + 8700x + -3x2 Solving for variable 'x'. Reorder the terms: 4857500 + x + -8700x + 3x2 = -4857500 + 8700x + -3x2 + 4857500 + -8700x + 3x2 Combine like terms: x + -8700x = -8699x 4857500 + -8699x + 3x2 = -4857500 + 8700x + -3x2 + 4857500 + -8700x + 3x2 Reorder the terms: 4857500 + -8699x + 3x2 = -4857500 + 4857500 + 8700x + -8700x + -3x2 + 3x2 Combine like terms: -4857500 + 4857500 = 0 4857500 + -8699x + 3x2 = 0 + 8700x + -8700x + -3x2 + 3x2 4857500 + -8699x + 3x2 = 8700x + -8700x + -3x2 + 3x2 Combine like terms: 8700x + -8700x = 0 4857500 + -8699x + 3x2 = 0 + -3x2 + 3x2 4857500 + -8699x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 4857500 + -8699x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1619166.667 + -2899.666667x + x2 = 0 Move the constant term to the right: Add '-1619166.667' to each side of the equation. 1619166.667 + -2899.666667x + -1619166.667 + x2 = 0 + -1619166.667 Reorder the terms: 1619166.667 + -1619166.667 + -2899.666667x + x2 = 0 + -1619166.667 Combine like terms: 1619166.667 + -1619166.667 = 0.000 0.000 + -2899.666667x + x2 = 0 + -1619166.667 -2899.666667x + x2 = 0 + -1619166.667 Combine like terms: 0 + -1619166.667 = -1619166.667 -2899.666667x + x2 = -1619166.667 The x term is -2899.666667x. Take half its coefficient (-1449.833334). Square it (2102016.696) and add it to both sides. Add '2102016.696' to each side of the equation. -2899.666667x + 2102016.696 + x2 = -1619166.667 + 2102016.696 Reorder the terms: 2102016.696 + -2899.666667x + x2 = -1619166.667 + 2102016.696 Combine like terms: -1619166.667 + 2102016.696 = 482850.029 2102016.696 + -2899.666667x + x2 = 482850.029 Factor a perfect square on the left side: (x + -1449.833334)(x + -1449.833334) = 482850.029 Calculate the square root of the right side: 694.874110181 Break this problem into two subproblems by setting (x + -1449.833334) equal to 694.874110181 and -694.874110181.Subproblem 1
x + -1449.833334 = 694.874110181 Simplifying x + -1449.833334 = 694.874110181 Reorder the terms: -1449.833334 + x = 694.874110181 Solving -1449.833334 + x = 694.874110181 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1449.833334' to each side of the equation. -1449.833334 + 1449.833334 + x = 694.874110181 + 1449.833334 Combine like terms: -1449.833334 + 1449.833334 = 0.000000 0.000000 + x = 694.874110181 + 1449.833334 x = 694.874110181 + 1449.833334 Combine like terms: 694.874110181 + 1449.833334 = 2144.707444181 x = 2144.707444181 Simplifying x = 2144.707444181Subproblem 2
x + -1449.833334 = -694.874110181 Simplifying x + -1449.833334 = -694.874110181 Reorder the terms: -1449.833334 + x = -694.874110181 Solving -1449.833334 + x = -694.874110181 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1449.833334' to each side of the equation. -1449.833334 + 1449.833334 + x = -694.874110181 + 1449.833334 Combine like terms: -1449.833334 + 1449.833334 = 0.000000 0.000000 + x = -694.874110181 + 1449.833334 x = -694.874110181 + 1449.833334 Combine like terms: -694.874110181 + 1449.833334 = 754.959223819 x = 754.959223819 Simplifying x = 754.959223819Solution
The solution to the problem is based on the solutions from the subproblems. x = {2144.707444181, 754.959223819}
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