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Simplifying 3x2 + 12000x + -2000 = 0 Reorder the terms: -2000 + 12000x + 3x2 = 0 Solving -2000 + 12000x + 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'. -666.6666667 + 4000x + x2 = 0 Move the constant term to the right: Add '666.6666667' to each side of the equation. -666.6666667 + 4000x + 666.6666667 + x2 = 0 + 666.6666667 Reorder the terms: -666.6666667 + 666.6666667 + 4000x + x2 = 0 + 666.6666667 Combine like terms: -666.6666667 + 666.6666667 = 0.0000000 0.0000000 + 4000x + x2 = 0 + 666.6666667 4000x + x2 = 0 + 666.6666667 Combine like terms: 0 + 666.6666667 = 666.6666667 4000x + x2 = 666.6666667 The x term is 4000x. Take half its coefficient (2000). Square it (4000000) and add it to both sides. Add '4000000' to each side of the equation. 4000x + 4000000 + x2 = 666.6666667 + 4000000 Reorder the terms: 4000000 + 4000x + x2 = 666.6666667 + 4000000 Combine like terms: 666.6666667 + 4000000 = 4000666.6666667 4000000 + 4000x + x2 = 4000666.6666667 Factor a perfect square on the left side: (x + 2000)(x + 2000) = 4000666.6666667 Calculate the square root of the right side: 2000.166659723 Break this problem into two subproblems by setting (x + 2000) equal to 2000.166659723 and -2000.166659723.Subproblem 1
x + 2000 = 2000.166659723 Simplifying x + 2000 = 2000.166659723 Reorder the terms: 2000 + x = 2000.166659723 Solving 2000 + x = 2000.166659723 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2000' to each side of the equation. 2000 + -2000 + x = 2000.166659723 + -2000 Combine like terms: 2000 + -2000 = 0 0 + x = 2000.166659723 + -2000 x = 2000.166659723 + -2000 Combine like terms: 2000.166659723 + -2000 = 0.166659723 x = 0.166659723 Simplifying x = 0.166659723Subproblem 2
x + 2000 = -2000.166659723 Simplifying x + 2000 = -2000.166659723 Reorder the terms: 2000 + x = -2000.166659723 Solving 2000 + x = -2000.166659723 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2000' to each side of the equation. 2000 + -2000 + x = -2000.166659723 + -2000 Combine like terms: 2000 + -2000 = 0 0 + x = -2000.166659723 + -2000 x = -2000.166659723 + -2000 Combine like terms: -2000.166659723 + -2000 = -4000.166659723 x = -4000.166659723 Simplifying x = -4000.166659723Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.166659723, -4000.166659723}
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