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Simplifying 50000 = 20x + -0.001x2 Solving 50000 = 20x + -0.001x2 Solving for variable 'x'. Reorder the terms: 50000 + -20x + 0.001x2 = 20x + -20x + -0.001x2 + 0.001x2 Combine like terms: 20x + -20x = 0 50000 + -20x + 0.001x2 = 0 + -0.001x2 + 0.001x2 50000 + -20x + 0.001x2 = -0.001x2 + 0.001x2 Combine like terms: -0.001x2 + 0.001x2 = 0.000 50000 + -20x + 0.001x2 = 0.000 Begin completing the square. Divide all terms by 0.001 the coefficient of the squared term: Divide each side by '0.001'. 50000000 + -20000x + x2 = 0 Move the constant term to the right: Add '-50000000' to each side of the equation. 50000000 + -20000x + -50000000 + x2 = 0 + -50000000 Reorder the terms: 50000000 + -50000000 + -20000x + x2 = 0 + -50000000 Combine like terms: 50000000 + -50000000 = 0 0 + -20000x + x2 = 0 + -50000000 -20000x + x2 = 0 + -50000000 Combine like terms: 0 + -50000000 = -50000000 -20000x + x2 = -50000000 The x term is -20000x. Take half its coefficient (-10000). Square it (100000000) and add it to both sides. Add '100000000' to each side of the equation. -20000x + 100000000 + x2 = -50000000 + 100000000 Reorder the terms: 100000000 + -20000x + x2 = -50000000 + 100000000 Combine like terms: -50000000 + 100000000 = 50000000 100000000 + -20000x + x2 = 50000000 Factor a perfect square on the left side: (x + -10000)(x + -10000) = 50000000 Calculate the square root of the right side: 7071.067811865 Break this problem into two subproblems by setting (x + -10000) equal to 7071.067811865 and -7071.067811865.Subproblem 1
x + -10000 = 7071.067811865 Simplifying x + -10000 = 7071.067811865 Reorder the terms: -10000 + x = 7071.067811865 Solving -10000 + x = 7071.067811865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10000' to each side of the equation. -10000 + 10000 + x = 7071.067811865 + 10000 Combine like terms: -10000 + 10000 = 0 0 + x = 7071.067811865 + 10000 x = 7071.067811865 + 10000 Combine like terms: 7071.067811865 + 10000 = 17071.067811865 x = 17071.067811865 Simplifying x = 17071.067811865Subproblem 2
x + -10000 = -7071.067811865 Simplifying x + -10000 = -7071.067811865 Reorder the terms: -10000 + x = -7071.067811865 Solving -10000 + x = -7071.067811865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10000' to each side of the equation. -10000 + 10000 + x = -7071.067811865 + 10000 Combine like terms: -10000 + 10000 = 0 0 + x = -7071.067811865 + 10000 x = -7071.067811865 + 10000 Combine like terms: -7071.067811865 + 10000 = 2928.932188135 x = 2928.932188135 Simplifying x = 2928.932188135Solution
The solution to the problem is based on the solutions from the subproblems. x = {17071.067811865, 2928.932188135}
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