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Simplifying 0.0003x2 + 2x + 500 = 0 Reorder the terms: 500 + 2x + 0.0003x2 = 0 Solving 500 + 2x + 0.0003x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0003 the coefficient of the squared term: Divide each side by '0.0003'. 1666666.667 + 6666.666667x + x2 = 0 Move the constant term to the right: Add '-1666666.667' to each side of the equation. 1666666.667 + 6666.666667x + -1666666.667 + x2 = 0 + -1666666.667 Reorder the terms: 1666666.667 + -1666666.667 + 6666.666667x + x2 = 0 + -1666666.667 Combine like terms: 1666666.667 + -1666666.667 = 0.000 0.000 + 6666.666667x + x2 = 0 + -1666666.667 6666.666667x + x2 = 0 + -1666666.667 Combine like terms: 0 + -1666666.667 = -1666666.667 6666.666667x + x2 = -1666666.667 The x term is 6666.666667x. Take half its coefficient (3333.333334). Square it (11111111.12) and add it to both sides. Add '11111111.12' to each side of the equation. 6666.666667x + 11111111.12 + x2 = -1666666.667 + 11111111.12 Reorder the terms: 11111111.12 + 6666.666667x + x2 = -1666666.667 + 11111111.12 Combine like terms: -1666666.667 + 11111111.12 = 9444444.453 11111111.12 + 6666.666667x + x2 = 9444444.453 Factor a perfect square on the left side: (x + 3333.333334)(x + 3333.333334) = 9444444.453 Calculate the square root of the right side: 3073.181487156 Break this problem into two subproblems by setting (x + 3333.333334) equal to 3073.181487156 and -3073.181487156.Subproblem 1
x + 3333.333334 = 3073.181487156 Simplifying x + 3333.333334 = 3073.181487156 Reorder the terms: 3333.333334 + x = 3073.181487156 Solving 3333.333334 + x = 3073.181487156 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3333.333334' to each side of the equation. 3333.333334 + -3333.333334 + x = 3073.181487156 + -3333.333334 Combine like terms: 3333.333334 + -3333.333334 = 0.000000 0.000000 + x = 3073.181487156 + -3333.333334 x = 3073.181487156 + -3333.333334 Combine like terms: 3073.181487156 + -3333.333334 = -260.151846844 x = -260.151846844 Simplifying x = -260.151846844Subproblem 2
x + 3333.333334 = -3073.181487156 Simplifying x + 3333.333334 = -3073.181487156 Reorder the terms: 3333.333334 + x = -3073.181487156 Solving 3333.333334 + x = -3073.181487156 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3333.333334' to each side of the equation. 3333.333334 + -3333.333334 + x = -3073.181487156 + -3333.333334 Combine like terms: 3333.333334 + -3333.333334 = 0.000000 0.000000 + x = -3073.181487156 + -3333.333334 x = -3073.181487156 + -3333.333334 Combine like terms: -3073.181487156 + -3333.333334 = -6406.514821156 x = -6406.514821156 Simplifying x = -6406.514821156Solution
The solution to the problem is based on the solutions from the subproblems. x = {-260.151846844, -6406.514821156}
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