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Simplifying -0.000003x2 + 0.002x + 5 = 0 Reorder the terms: 5 + 0.002x + -0.000003x2 = 0 Solving 5 + 0.002x + -0.000003x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.000003 the coefficient of the squared term: Divide each side by '-0.000003'. -1666666.667 + -666.6666667x + x2 = 0 Move the constant term to the right: Add '1666666.667' to each side of the equation. -1666666.667 + -666.6666667x + 1666666.667 + x2 = 0 + 1666666.667 Reorder the terms: -1666666.667 + 1666666.667 + -666.6666667x + x2 = 0 + 1666666.667 Combine like terms: -1666666.667 + 1666666.667 = 0.000 0.000 + -666.6666667x + x2 = 0 + 1666666.667 -666.6666667x + x2 = 0 + 1666666.667 Combine like terms: 0 + 1666666.667 = 1666666.667 -666.6666667x + x2 = 1666666.667 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 = 1666666.667 + 111111.1112 Reorder the terms: 111111.1112 + -666.6666667x + x2 = 1666666.667 + 111111.1112 Combine like terms: 1666666.667 + 111111.1112 = 1777777.7782 111111.1112 + -666.6666667x + x2 = 1777777.7782 Factor a perfect square on the left side: (x + -333.3333334)(x + -333.3333334) = 1777777.7782 Calculate the square root of the right side: 1333.333333492 Break this problem into two subproblems by setting (x + -333.3333334) equal to 1333.333333492 and -1333.333333492.Subproblem 1
x + -333.3333334 = 1333.333333492 Simplifying x + -333.3333334 = 1333.333333492 Reorder the terms: -333.3333334 + x = 1333.333333492 Solving -333.3333334 + x = 1333.333333492 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 = 1333.333333492 + 333.3333334 Combine like terms: -333.3333334 + 333.3333334 = 0.0000000 0.0000000 + x = 1333.333333492 + 333.3333334 x = 1333.333333492 + 333.3333334 Combine like terms: 1333.333333492 + 333.3333334 = 1666.666666892 x = 1666.666666892 Simplifying x = 1666.666666892Subproblem 2
x + -333.3333334 = -1333.333333492 Simplifying x + -333.3333334 = -1333.333333492 Reorder the terms: -333.3333334 + x = -1333.333333492 Solving -333.3333334 + x = -1333.333333492 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 = -1333.333333492 + 333.3333334 Combine like terms: -333.3333334 + 333.3333334 = 0.0000000 0.0000000 + x = -1333.333333492 + 333.3333334 x = -1333.333333492 + 333.3333334 Combine like terms: -1333.333333492 + 333.3333334 = -1000.000000092 x = -1000.000000092 Simplifying x = -1000.000000092Solution
The solution to the problem is based on the solutions from the subproblems. x = {1666.666666892, -1000.000000092}
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