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Simplifying 3x2 + -2000x + 9 = 0 Reorder the terms: 9 + -2000x + 3x2 = 0 Solving 9 + -2000x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3 + -666.6666667x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -666.6666667x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -666.6666667x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -666.6666667x + x2 = 0 + -3 -666.6666667x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -666.6666667x + x2 = -3 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 = -3 + 111111.1112 Reorder the terms: 111111.1112 + -666.6666667x + x2 = -3 + 111111.1112 Combine like terms: -3 + 111111.1112 = 111108.1112 111111.1112 + -666.6666667x + x2 = 111108.1112 Factor a perfect square on the left side: (x + -333.3333334)(x + -333.3333334) = 111108.1112 Calculate the square root of the right side: 333.328833436 Break this problem into two subproblems by setting (x + -333.3333334) equal to 333.328833436 and -333.328833436.Subproblem 1
x + -333.3333334 = 333.328833436 Simplifying x + -333.3333334 = 333.328833436 Reorder the terms: -333.3333334 + x = 333.328833436 Solving -333.3333334 + x = 333.328833436 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 = 333.328833436 + 333.3333334 Combine like terms: -333.3333334 + 333.3333334 = 0.0000000 0.0000000 + x = 333.328833436 + 333.3333334 x = 333.328833436 + 333.3333334 Combine like terms: 333.328833436 + 333.3333334 = 666.662166836 x = 666.662166836 Simplifying x = 666.662166836Subproblem 2
x + -333.3333334 = -333.328833436 Simplifying x + -333.3333334 = -333.328833436 Reorder the terms: -333.3333334 + x = -333.328833436 Solving -333.3333334 + x = -333.328833436 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 = -333.328833436 + 333.3333334 Combine like terms: -333.3333334 + 333.3333334 = 0.0000000 0.0000000 + x = -333.328833436 + 333.3333334 x = -333.328833436 + 333.3333334 Combine like terms: -333.328833436 + 333.3333334 = 0.004499964 x = 0.004499964 Simplifying x = 0.004499964Solution
The solution to the problem is based on the solutions from the subproblems. x = {666.662166836, 0.004499964}
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