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Simplifying 0.0001x2 + 0.05x + -2.1 = 0 Reorder the terms: -2.1 + 0.05x + 0.0001x2 = 0 Solving -2.1 + 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'. -21000 + 500x + x2 = 0 Move the constant term to the right: Add '21000' to each side of the equation. -21000 + 500x + 21000 + x2 = 0 + 21000 Reorder the terms: -21000 + 21000 + 500x + x2 = 0 + 21000 Combine like terms: -21000 + 21000 = 0 0 + 500x + x2 = 0 + 21000 500x + x2 = 0 + 21000 Combine like terms: 0 + 21000 = 21000 500x + x2 = 21000 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 = 21000 + 62500 Reorder the terms: 62500 + 500x + x2 = 21000 + 62500 Combine like terms: 21000 + 62500 = 83500 62500 + 500x + x2 = 83500 Factor a perfect square on the left side: (x + 250)(x + 250) = 83500 Calculate the square root of the right side: 288.963665536 Break this problem into two subproblems by setting (x + 250) equal to 288.963665536 and -288.963665536.Subproblem 1
x + 250 = 288.963665536 Simplifying x + 250 = 288.963665536 Reorder the terms: 250 + x = 288.963665536 Solving 250 + x = 288.963665536 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 = 288.963665536 + -250 Combine like terms: 250 + -250 = 0 0 + x = 288.963665536 + -250 x = 288.963665536 + -250 Combine like terms: 288.963665536 + -250 = 38.963665536 x = 38.963665536 Simplifying x = 38.963665536Subproblem 2
x + 250 = -288.963665536 Simplifying x + 250 = -288.963665536 Reorder the terms: 250 + x = -288.963665536 Solving 250 + x = -288.963665536 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 = -288.963665536 + -250 Combine like terms: 250 + -250 = 0 0 + x = -288.963665536 + -250 x = -288.963665536 + -250 Combine like terms: -288.963665536 + -250 = -538.963665536 x = -538.963665536 Simplifying x = -538.963665536Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.963665536, -538.963665536}
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