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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 = 43500 62500 + -500x + x2 = 43500 Factor a perfect square on the left side: (x + -250)(x + -250) = 43500 Calculate the square root of the right side: 208.566536146 Break this problem into two subproblems by setting (x + -250) equal to 208.566536146 and -208.566536146.Subproblem 1
x + -250 = 208.566536146 Simplifying x + -250 = 208.566536146 Reorder the terms: -250 + x = 208.566536146 Solving -250 + x = 208.566536146 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 = 208.566536146 + 250 Combine like terms: -250 + 250 = 0 0 + x = 208.566536146 + 250 x = 208.566536146 + 250 Combine like terms: 208.566536146 + 250 = 458.566536146 x = 458.566536146 Simplifying x = 458.566536146Subproblem 2
x + -250 = -208.566536146 Simplifying x + -250 = -208.566536146 Reorder the terms: -250 + x = -208.566536146 Solving -250 + x = -208.566536146 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 = -208.566536146 + 250 Combine like terms: -250 + 250 = 0 0 + x = -208.566536146 + 250 x = -208.566536146 + 250 Combine like terms: -208.566536146 + 250 = 41.433463854 x = 41.433463854 Simplifying x = 41.433463854Solution
The solution to the problem is based on the solutions from the subproblems. x = {458.566536146, 41.433463854}
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