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Simplifying x + -1(50 + 0.2x) * x = 200 Reorder the terms for easier multiplication: x + -1x(50 + 0.2x) = 200 x + (50 * -1x + 0.2x * -1x) = 200 x + (-50x + -0.2x2) = 200 Combine like terms: x + -50x = -49x -49x + -0.2x2 = 200 Solving -49x + -0.2x2 = 200 Solving for variable 'x'. Reorder the terms: -200 + -49x + -0.2x2 = 200 + -200 Combine like terms: 200 + -200 = 0 -200 + -49x + -0.2x2 = 0 Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. 1000 + 245x + x2 = 0 Move the constant term to the right: Add '-1000' to each side of the equation. 1000 + 245x + -1000 + x2 = 0 + -1000 Reorder the terms: 1000 + -1000 + 245x + x2 = 0 + -1000 Combine like terms: 1000 + -1000 = 0 0 + 245x + x2 = 0 + -1000 245x + x2 = 0 + -1000 Combine like terms: 0 + -1000 = -1000 245x + x2 = -1000 The x term is 245x. Take half its coefficient (122.5). Square it (15006.25) and add it to both sides. Add '15006.25' to each side of the equation. 245x + 15006.25 + x2 = -1000 + 15006.25 Reorder the terms: 15006.25 + 245x + x2 = -1000 + 15006.25 Combine like terms: -1000 + 15006.25 = 14006.25 15006.25 + 245x + x2 = 14006.25 Factor a perfect square on the left side: (x + 122.5)(x + 122.5) = 14006.25 Calculate the square root of the right side: 118.348003785 Break this problem into two subproblems by setting (x + 122.5) equal to 118.348003785 and -118.348003785.Subproblem 1
x + 122.5 = 118.348003785 Simplifying x + 122.5 = 118.348003785 Reorder the terms: 122.5 + x = 118.348003785 Solving 122.5 + x = 118.348003785 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-122.5' to each side of the equation. 122.5 + -122.5 + x = 118.348003785 + -122.5 Combine like terms: 122.5 + -122.5 = 0.0 0.0 + x = 118.348003785 + -122.5 x = 118.348003785 + -122.5 Combine like terms: 118.348003785 + -122.5 = -4.151996215 x = -4.151996215 Simplifying x = -4.151996215Subproblem 2
x + 122.5 = -118.348003785 Simplifying x + 122.5 = -118.348003785 Reorder the terms: 122.5 + x = -118.348003785 Solving 122.5 + x = -118.348003785 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-122.5' to each side of the equation. 122.5 + -122.5 + x = -118.348003785 + -122.5 Combine like terms: 122.5 + -122.5 = 0.0 0.0 + x = -118.348003785 + -122.5 x = -118.348003785 + -122.5 Combine like terms: -118.348003785 + -122.5 = -240.848003785 x = -240.848003785 Simplifying x = -240.848003785Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.151996215, -240.848003785}
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