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Simplifying 0.0001x2 + 0.02x + -2 = 0 Reorder the terms: -2 + 0.02x + 0.0001x2 = 0 Solving -2 + 0.02x + 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'. -20000 + 200x + x2 = 0 Move the constant term to the right: Add '20000' to each side of the equation. -20000 + 200x + 20000 + x2 = 0 + 20000 Reorder the terms: -20000 + 20000 + 200x + x2 = 0 + 20000 Combine like terms: -20000 + 20000 = 0 0 + 200x + x2 = 0 + 20000 200x + x2 = 0 + 20000 Combine like terms: 0 + 20000 = 20000 200x + x2 = 20000 The x term is 200x. Take half its coefficient (100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. 200x + 10000 + x2 = 20000 + 10000 Reorder the terms: 10000 + 200x + x2 = 20000 + 10000 Combine like terms: 20000 + 10000 = 30000 10000 + 200x + x2 = 30000 Factor a perfect square on the left side: (x + 100)(x + 100) = 30000 Calculate the square root of the right side: 173.205080757 Break this problem into two subproblems by setting (x + 100) equal to 173.205080757 and -173.205080757.Subproblem 1
x + 100 = 173.205080757 Simplifying x + 100 = 173.205080757 Reorder the terms: 100 + x = 173.205080757 Solving 100 + x = 173.205080757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + x = 173.205080757 + -100 Combine like terms: 100 + -100 = 0 0 + x = 173.205080757 + -100 x = 173.205080757 + -100 Combine like terms: 173.205080757 + -100 = 73.205080757 x = 73.205080757 Simplifying x = 73.205080757Subproblem 2
x + 100 = -173.205080757 Simplifying x + 100 = -173.205080757 Reorder the terms: 100 + x = -173.205080757 Solving 100 + x = -173.205080757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + x = -173.205080757 + -100 Combine like terms: 100 + -100 = 0 0 + x = -173.205080757 + -100 x = -173.205080757 + -100 Combine like terms: -173.205080757 + -100 = -273.205080757 x = -273.205080757 Simplifying x = -273.205080757Solution
The solution to the problem is based on the solutions from the subproblems. x = {73.205080757, -273.205080757}
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