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Simplifying -0.001x2 + 10x + -1000 + -10000 = 0 Reorder the terms: -1000 + -10000 + 10x + -0.001x2 = 0 Combine like terms: -1000 + -10000 = -11000 -11000 + 10x + -0.001x2 = 0 Solving -11000 + 10x + -0.001x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.001 the coefficient of the squared term: Divide each side by '-0.001'. 11000000 + -10000x + x2 = 0 Move the constant term to the right: Add '-11000000' to each side of the equation. 11000000 + -10000x + -11000000 + x2 = 0 + -11000000 Reorder the terms: 11000000 + -11000000 + -10000x + x2 = 0 + -11000000 Combine like terms: 11000000 + -11000000 = 0 0 + -10000x + x2 = 0 + -11000000 -10000x + x2 = 0 + -11000000 Combine like terms: 0 + -11000000 = -11000000 -10000x + x2 = -11000000 The x term is -10000x. Take half its coefficient (-5000). Square it (25000000) and add it to both sides. Add '25000000' to each side of the equation. -10000x + 25000000 + x2 = -11000000 + 25000000 Reorder the terms: 25000000 + -10000x + x2 = -11000000 + 25000000 Combine like terms: -11000000 + 25000000 = 14000000 25000000 + -10000x + x2 = 14000000 Factor a perfect square on the left side: (x + -5000)(x + -5000) = 14000000 Calculate the square root of the right side: 3741.657386774 Break this problem into two subproblems by setting (x + -5000) equal to 3741.657386774 and -3741.657386774.Subproblem 1
x + -5000 = 3741.657386774 Simplifying x + -5000 = 3741.657386774 Reorder the terms: -5000 + x = 3741.657386774 Solving -5000 + x = 3741.657386774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5000' to each side of the equation. -5000 + 5000 + x = 3741.657386774 + 5000 Combine like terms: -5000 + 5000 = 0 0 + x = 3741.657386774 + 5000 x = 3741.657386774 + 5000 Combine like terms: 3741.657386774 + 5000 = 8741.657386774 x = 8741.657386774 Simplifying x = 8741.657386774Subproblem 2
x + -5000 = -3741.657386774 Simplifying x + -5000 = -3741.657386774 Reorder the terms: -5000 + x = -3741.657386774 Solving -5000 + x = -3741.657386774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5000' to each side of the equation. -5000 + 5000 + x = -3741.657386774 + 5000 Combine like terms: -5000 + 5000 = 0 0 + x = -3741.657386774 + 5000 x = -3741.657386774 + 5000 Combine like terms: -3741.657386774 + 5000 = 1258.342613226 x = 1258.342613226 Simplifying x = 1258.342613226Solution
The solution to the problem is based on the solutions from the subproblems. x = {8741.657386774, 1258.342613226}
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