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Simplifying 0.0015x2 + -1x + 125 = 0 Reorder the terms: 125 + -1x + 0.0015x2 = 0 Solving 125 + -1x + 0.0015x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0015 the coefficient of the squared term: Divide each side by '0.0015'. 83333.33333 + -666.6666667x + x2 = 0 Move the constant term to the right: Add '-83333.33333' to each side of the equation. 83333.33333 + -666.6666667x + -83333.33333 + x2 = 0 + -83333.33333 Reorder the terms: 83333.33333 + -83333.33333 + -666.6666667x + x2 = 0 + -83333.33333 Combine like terms: 83333.33333 + -83333.33333 = 0.00000 0.00000 + -666.6666667x + x2 = 0 + -83333.33333 -666.6666667x + x2 = 0 + -83333.33333 Combine like terms: 0 + -83333.33333 = -83333.33333 -666.6666667x + x2 = -83333.33333 The x term is -666.6666667x. Take half its coefficient (-333.3333334). Square it (111111.1112) and add it to both sides. Add '111111.1112' to each side of the equation. -666.6666667x + 111111.1112 + x2 = -83333.33333 + 111111.1112 Reorder the terms: 111111.1112 + -666.6666667x + x2 = -83333.33333 + 111111.1112 Combine like terms: -83333.33333 + 111111.1112 = 27777.77787 111111.1112 + -666.6666667x + x2 = 27777.77787 Factor a perfect square on the left side: (x + -333.3333334)(x + -333.3333334) = 27777.77787 Calculate the square root of the right side: 166.666666943 Break this problem into two subproblems by setting (x + -333.3333334) equal to 166.666666943 and -166.666666943.Subproblem 1
x + -333.3333334 = 166.666666943 Simplifying x + -333.3333334 = 166.666666943 Reorder the terms: -333.3333334 + x = 166.666666943 Solving -333.3333334 + x = 166.666666943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '333.3333334' to each side of the equation. -333.3333334 + 333.3333334 + x = 166.666666943 + 333.3333334 Combine like terms: -333.3333334 + 333.3333334 = 0.0000000 0.0000000 + x = 166.666666943 + 333.3333334 x = 166.666666943 + 333.3333334 Combine like terms: 166.666666943 + 333.3333334 = 500.000000343 x = 500.000000343 Simplifying x = 500.000000343Subproblem 2
x + -333.3333334 = -166.666666943 Simplifying x + -333.3333334 = -166.666666943 Reorder the terms: -333.3333334 + x = -166.666666943 Solving -333.3333334 + x = -166.666666943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '333.3333334' to each side of the equation. -333.3333334 + 333.3333334 + x = -166.666666943 + 333.3333334 Combine like terms: -333.3333334 + 333.3333334 = 0.0000000 0.0000000 + x = -166.666666943 + 333.3333334 x = -166.666666943 + 333.3333334 Combine like terms: -166.666666943 + 333.3333334 = 166.666666457 x = 166.666666457 Simplifying x = 166.666666457Solution
The solution to the problem is based on the solutions from the subproblems. x = {500.000000343, 166.666666457}
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