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Simplifying x2 + -50x + 200 = 0 Reorder the terms: 200 + -50x + x2 = 0 Solving 200 + -50x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-200' to each side of the equation. 200 + -50x + -200 + x2 = 0 + -200 Reorder the terms: 200 + -200 + -50x + x2 = 0 + -200 Combine like terms: 200 + -200 = 0 0 + -50x + x2 = 0 + -200 -50x + x2 = 0 + -200 Combine like terms: 0 + -200 = -200 -50x + x2 = -200 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = -200 + 625 Reorder the terms: 625 + -50x + x2 = -200 + 625 Combine like terms: -200 + 625 = 425 625 + -50x + x2 = 425 Factor a perfect square on the left side: (x + -25)(x + -25) = 425 Calculate the square root of the right side: 20.615528128 Break this problem into two subproblems by setting (x + -25) equal to 20.615528128 and -20.615528128.Subproblem 1
x + -25 = 20.615528128 Simplifying x + -25 = 20.615528128 Reorder the terms: -25 + x = 20.615528128 Solving -25 + x = 20.615528128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 20.615528128 + 25 Combine like terms: -25 + 25 = 0 0 + x = 20.615528128 + 25 x = 20.615528128 + 25 Combine like terms: 20.615528128 + 25 = 45.615528128 x = 45.615528128 Simplifying x = 45.615528128Subproblem 2
x + -25 = -20.615528128 Simplifying x + -25 = -20.615528128 Reorder the terms: -25 + x = -20.615528128 Solving -25 + x = -20.615528128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -20.615528128 + 25 Combine like terms: -25 + 25 = 0 0 + x = -20.615528128 + 25 x = -20.615528128 + 25 Combine like terms: -20.615528128 + 25 = 4.384471872 x = 4.384471872 Simplifying x = 4.384471872Solution
The solution to the problem is based on the solutions from the subproblems. x = {45.615528128, 4.384471872}
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