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Simplifying 0.0001x2 + 0.05x + -1.9 = 0 Reorder the terms: -1.9 + 0.05x + 0.0001x2 = 0 Solving -1.9 + 0.05x + 0.0001x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0001 the coefficient of the squared term: Divide each side by '0.0001'. -19000 + 500x + x2 = 0 Move the constant term to the right: Add '19000' to each side of the equation. -19000 + 500x + 19000 + x2 = 0 + 19000 Reorder the terms: -19000 + 19000 + 500x + x2 = 0 + 19000 Combine like terms: -19000 + 19000 = 0 0 + 500x + x2 = 0 + 19000 500x + x2 = 0 + 19000 Combine like terms: 0 + 19000 = 19000 500x + x2 = 19000 The x term is 500x. Take half its coefficient (250). Square it (62500) and add it to both sides. Add '62500' to each side of the equation. 500x + 62500 + x2 = 19000 + 62500 Reorder the terms: 62500 + 500x + x2 = 19000 + 62500 Combine like terms: 19000 + 62500 = 81500 62500 + 500x + x2 = 81500 Factor a perfect square on the left side: (x + 250)(x + 250) = 81500 Calculate the square root of the right side: 285.482048472 Break this problem into two subproblems by setting (x + 250) equal to 285.482048472 and -285.482048472.Subproblem 1
x + 250 = 285.482048472 Simplifying x + 250 = 285.482048472 Reorder the terms: 250 + x = 285.482048472 Solving 250 + x = 285.482048472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-250' to each side of the equation. 250 + -250 + x = 285.482048472 + -250 Combine like terms: 250 + -250 = 0 0 + x = 285.482048472 + -250 x = 285.482048472 + -250 Combine like terms: 285.482048472 + -250 = 35.482048472 x = 35.482048472 Simplifying x = 35.482048472Subproblem 2
x + 250 = -285.482048472 Simplifying x + 250 = -285.482048472 Reorder the terms: 250 + x = -285.482048472 Solving 250 + x = -285.482048472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-250' to each side of the equation. 250 + -250 + x = -285.482048472 + -250 Combine like terms: 250 + -250 = 0 0 + x = -285.482048472 + -250 x = -285.482048472 + -250 Combine like terms: -285.482048472 + -250 = -535.482048472 x = -535.482048472 Simplifying x = -535.482048472Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.482048472, -535.482048472}
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