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Simplifying 0.0001x2 + 0.05x + -2.2 = 0 Reorder the terms: -2.2 + 0.05x + 0.0001x2 = 0 Solving -2.2 + 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'. -22000 + 500x + x2 = 0 Move the constant term to the right: Add '22000' to each side of the equation. -22000 + 500x + 22000 + x2 = 0 + 22000 Reorder the terms: -22000 + 22000 + 500x + x2 = 0 + 22000 Combine like terms: -22000 + 22000 = 0 0 + 500x + x2 = 0 + 22000 500x + x2 = 0 + 22000 Combine like terms: 0 + 22000 = 22000 500x + x2 = 22000 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 = 22000 + 62500 Reorder the terms: 62500 + 500x + x2 = 22000 + 62500 Combine like terms: 22000 + 62500 = 84500 62500 + 500x + x2 = 84500 Factor a perfect square on the left side: (x + 250)(x + 250) = 84500 Calculate the square root of the right side: 290.688837075 Break this problem into two subproblems by setting (x + 250) equal to 290.688837075 and -290.688837075.Subproblem 1
x + 250 = 290.688837075 Simplifying x + 250 = 290.688837075 Reorder the terms: 250 + x = 290.688837075 Solving 250 + x = 290.688837075 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 = 290.688837075 + -250 Combine like terms: 250 + -250 = 0 0 + x = 290.688837075 + -250 x = 290.688837075 + -250 Combine like terms: 290.688837075 + -250 = 40.688837075 x = 40.688837075 Simplifying x = 40.688837075Subproblem 2
x + 250 = -290.688837075 Simplifying x + 250 = -290.688837075 Reorder the terms: 250 + x = -290.688837075 Solving 250 + x = -290.688837075 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 = -290.688837075 + -250 Combine like terms: 250 + -250 = 0 0 + x = -290.688837075 + -250 x = -290.688837075 + -250 Combine like terms: -290.688837075 + -250 = -540.688837075 x = -540.688837075 Simplifying x = -540.688837075Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.688837075, -540.688837075}
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