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Simplifying 0.001x2 + 0.6x + 140 = 1000 Reorder the terms: 140 + 0.6x + 0.001x2 = 1000 Solving 140 + 0.6x + 0.001x2 = 1000 Solving for variable 'x'. Reorder the terms: 140 + -1000 + 0.6x + 0.001x2 = 1000 + -1000 Combine like terms: 140 + -1000 = -860 -860 + 0.6x + 0.001x2 = 1000 + -1000 Combine like terms: 1000 + -1000 = 0 -860 + 0.6x + 0.001x2 = 0 Begin completing the square. Divide all terms by 0.001 the coefficient of the squared term: Divide each side by '0.001'. -860000 + 600x + x2 = 0 Move the constant term to the right: Add '860000' to each side of the equation. -860000 + 600x + 860000 + x2 = 0 + 860000 Reorder the terms: -860000 + 860000 + 600x + x2 = 0 + 860000 Combine like terms: -860000 + 860000 = 0 0 + 600x + x2 = 0 + 860000 600x + x2 = 0 + 860000 Combine like terms: 0 + 860000 = 860000 600x + x2 = 860000 The x term is 600x. Take half its coefficient (300). Square it (90000) and add it to both sides. Add '90000' to each side of the equation. 600x + 90000 + x2 = 860000 + 90000 Reorder the terms: 90000 + 600x + x2 = 860000 + 90000 Combine like terms: 860000 + 90000 = 950000 90000 + 600x + x2 = 950000 Factor a perfect square on the left side: (x + 300)(x + 300) = 950000 Calculate the square root of the right side: 974.679434481 Break this problem into two subproblems by setting (x + 300) equal to 974.679434481 and -974.679434481.Subproblem 1
x + 300 = 974.679434481 Simplifying x + 300 = 974.679434481 Reorder the terms: 300 + x = 974.679434481 Solving 300 + x = 974.679434481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-300' to each side of the equation. 300 + -300 + x = 974.679434481 + -300 Combine like terms: 300 + -300 = 0 0 + x = 974.679434481 + -300 x = 974.679434481 + -300 Combine like terms: 974.679434481 + -300 = 674.679434481 x = 674.679434481 Simplifying x = 674.679434481Subproblem 2
x + 300 = -974.679434481 Simplifying x + 300 = -974.679434481 Reorder the terms: 300 + x = -974.679434481 Solving 300 + x = -974.679434481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-300' to each side of the equation. 300 + -300 + x = -974.679434481 + -300 Combine like terms: 300 + -300 = 0 0 + x = -974.679434481 + -300 x = -974.679434481 + -300 Combine like terms: -974.679434481 + -300 = -1274.679434481 x = -1274.679434481 Simplifying x = -1274.679434481Solution
The solution to the problem is based on the solutions from the subproblems. x = {674.679434481, -1274.679434481}
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