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Simplifying 0.003x2 + -6x + 3 = 0 Reorder the terms: 3 + -6x + 0.003x2 = 0 Solving 3 + -6x + 0.003x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.003 the coefficient of the squared term: Divide each side by '0.003'. 1000 + -2000x + x2 = 0 Move the constant term to the right: Add '-1000' to each side of the equation. 1000 + -2000x + -1000 + x2 = 0 + -1000 Reorder the terms: 1000 + -1000 + -2000x + x2 = 0 + -1000 Combine like terms: 1000 + -1000 = 0 0 + -2000x + x2 = 0 + -1000 -2000x + x2 = 0 + -1000 Combine like terms: 0 + -1000 = -1000 -2000x + x2 = -1000 The x term is -2000x. Take half its coefficient (-1000). Square it (1000000) and add it to both sides. Add '1000000' to each side of the equation. -2000x + 1000000 + x2 = -1000 + 1000000 Reorder the terms: 1000000 + -2000x + x2 = -1000 + 1000000 Combine like terms: -1000 + 1000000 = 999000 1000000 + -2000x + x2 = 999000 Factor a perfect square on the left side: (x + -1000)(x + -1000) = 999000 Calculate the square root of the right side: 999.499874937 Break this problem into two subproblems by setting (x + -1000) equal to 999.499874937 and -999.499874937.Subproblem 1
x + -1000 = 999.499874937 Simplifying x + -1000 = 999.499874937 Reorder the terms: -1000 + x = 999.499874937 Solving -1000 + x = 999.499874937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1000' to each side of the equation. -1000 + 1000 + x = 999.499874937 + 1000 Combine like terms: -1000 + 1000 = 0 0 + x = 999.499874937 + 1000 x = 999.499874937 + 1000 Combine like terms: 999.499874937 + 1000 = 1999.499874937 x = 1999.499874937 Simplifying x = 1999.499874937Subproblem 2
x + -1000 = -999.499874937 Simplifying x + -1000 = -999.499874937 Reorder the terms: -1000 + x = -999.499874937 Solving -1000 + x = -999.499874937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1000' to each side of the equation. -1000 + 1000 + x = -999.499874937 + 1000 Combine like terms: -1000 + 1000 = 0 0 + x = -999.499874937 + 1000 x = -999.499874937 + 1000 Combine like terms: -999.499874937 + 1000 = 0.500125063 x = 0.500125063 Simplifying x = 0.500125063Solution
The solution to the problem is based on the solutions from the subproblems. x = {1999.499874937, 0.500125063}
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