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Simplifying 1000x2 + 600x = x + -1 Reorder the terms: 600x + 1000x2 = x + -1 Reorder the terms: 600x + 1000x2 = -1 + x Solving 600x + 1000x2 = -1 + x Solving for variable 'x'. Reorder the terms: 1 + 600x + -1x + 1000x2 = -1 + x + 1 + -1x Combine like terms: 600x + -1x = 599x 1 + 599x + 1000x2 = -1 + x + 1 + -1x Reorder the terms: 1 + 599x + 1000x2 = -1 + 1 + x + -1x Combine like terms: -1 + 1 = 0 1 + 599x + 1000x2 = 0 + x + -1x 1 + 599x + 1000x2 = x + -1x Combine like terms: x + -1x = 0 1 + 599x + 1000x2 = 0 Begin completing the square. Divide all terms by 1000 the coefficient of the squared term: Divide each side by '1000'. 0.001 + 0.599x + x2 = 0 Move the constant term to the right: Add '-0.001' to each side of the equation. 0.001 + 0.599x + -0.001 + x2 = 0 + -0.001 Reorder the terms: 0.001 + -0.001 + 0.599x + x2 = 0 + -0.001 Combine like terms: 0.001 + -0.001 = 0.000 0.000 + 0.599x + x2 = 0 + -0.001 0.599x + x2 = 0 + -0.001 Combine like terms: 0 + -0.001 = -0.001 0.599x + x2 = -0.001 The x term is 0.599x. Take half its coefficient (0.2995). Square it (0.08970025) and add it to both sides. Add '0.08970025' to each side of the equation. 0.599x + 0.08970025 + x2 = -0.001 + 0.08970025 Reorder the terms: 0.08970025 + 0.599x + x2 = -0.001 + 0.08970025 Combine like terms: -0.001 + 0.08970025 = 0.08870025 0.08970025 + 0.599x + x2 = 0.08870025 Factor a perfect square on the left side: (x + 0.2995)(x + 0.2995) = 0.08870025 Calculate the square root of the right side: 0.297825872 Break this problem into two subproblems by setting (x + 0.2995) equal to 0.297825872 and -0.297825872.Subproblem 1
x + 0.2995 = 0.297825872 Simplifying x + 0.2995 = 0.297825872 Reorder the terms: 0.2995 + x = 0.297825872 Solving 0.2995 + x = 0.297825872 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2995' to each side of the equation. 0.2995 + -0.2995 + x = 0.297825872 + -0.2995 Combine like terms: 0.2995 + -0.2995 = 0.0000 0.0000 + x = 0.297825872 + -0.2995 x = 0.297825872 + -0.2995 Combine like terms: 0.297825872 + -0.2995 = -0.001674128 x = -0.001674128 Simplifying x = -0.001674128Subproblem 2
x + 0.2995 = -0.297825872 Simplifying x + 0.2995 = -0.297825872 Reorder the terms: 0.2995 + x = -0.297825872 Solving 0.2995 + x = -0.297825872 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2995' to each side of the equation. 0.2995 + -0.2995 + x = -0.297825872 + -0.2995 Combine like terms: 0.2995 + -0.2995 = 0.0000 0.0000 + x = -0.297825872 + -0.2995 x = -0.297825872 + -0.2995 Combine like terms: -0.297825872 + -0.2995 = -0.597325872 x = -0.597325872 Simplifying x = -0.597325872Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.001674128, -0.597325872}
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