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Simplifying 0.0002x2 + -20000x + 400000 = 0 Reorder the terms: 400000 + -20000x + 0.0002x2 = 0 Solving 400000 + -20000x + 0.0002x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0002 the coefficient of the squared term: Divide each side by '0.0002'. 2000000000 + -100000000x + x2 = 0 Move the constant term to the right: Add '-2000000000' to each side of the equation. 2000000000 + -100000000x + -2000000000 + x2 = 0 + -2000000000 Reorder the terms: 2000000000 + -2000000000 + -100000000x + x2 = 0 + -2000000000 Combine like terms: 2000000000 + -2000000000 = 0 0 + -100000000x + x2 = 0 + -2000000000 -100000000x + x2 = 0 + -2000000000 Combine like terms: 0 + -2000000000 = -2000000000 -100000000x + x2 = -2000000000 The x term is -100000000x. Take half its coefficient (-50000000). Square it (2500000000000000) and add it to both sides. Add '2500000000000000' to each side of the equation. -100000000x + 2500000000000000 + x2 = -2000000000 + 2500000000000000 Reorder the terms: 2500000000000000 + -100000000x + x2 = -2000000000 + 2500000000000000 Combine like terms: -2000000000 + 2500000000000000 = 2499998000000000 2500000000000000 + -100000000x + x2 = 2499998000000000 Factor a perfect square on the left side: (x + -50000000)(x + -50000000) = 2499998000000000 Calculate the square root of the right side: 49999979.999996 Break this problem into two subproblems by setting (x + -50000000) equal to 49999979.999996 and -49999979.999996.Subproblem 1
x + -50000000 = 49999979.999996 Simplifying x + -50000000 = 49999979.999996 Reorder the terms: -50000000 + x = 49999979.999996 Solving -50000000 + x = 49999979.999996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50000000' to each side of the equation. -50000000 + 50000000 + x = 49999979.999996 + 50000000 Combine like terms: -50000000 + 50000000 = 0 0 + x = 49999979.999996 + 50000000 x = 49999979.999996 + 50000000 Combine like terms: 49999979.999996 + 50000000 = 99999979.999996 x = 99999979.999996 Simplifying x = 99999979.999996Subproblem 2
x + -50000000 = -49999979.999996 Simplifying x + -50000000 = -49999979.999996 Reorder the terms: -50000000 + x = -49999979.999996 Solving -50000000 + x = -49999979.999996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50000000' to each side of the equation. -50000000 + 50000000 + x = -49999979.999996 + 50000000 Combine like terms: -50000000 + 50000000 = 0 0 + x = -49999979.999996 + 50000000 x = -49999979.999996 + 50000000 Combine like terms: -49999979.999996 + 50000000 = 20.000004 x = 20.000004 Simplifying x = 20.000004Solution
The solution to the problem is based on the solutions from the subproblems. x = {99999979.999996, 20.000004}
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