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Simplifying X2 + 50X = 250000 Reorder the terms: 50X + X2 = 250000 Solving 50X + X2 = 250000 Solving for variable 'X'. Reorder the terms: -250000 + 50X + X2 = 250000 + -250000 Combine like terms: 250000 + -250000 = 0 -250000 + 50X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '250000' to each side of the equation. -250000 + 50X + 250000 + X2 = 0 + 250000 Reorder the terms: -250000 + 250000 + 50X + X2 = 0 + 250000 Combine like terms: -250000 + 250000 = 0 0 + 50X + X2 = 0 + 250000 50X + X2 = 0 + 250000 Combine like terms: 0 + 250000 = 250000 50X + X2 = 250000 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 = 250000 + 625 Reorder the terms: 625 + 50X + X2 = 250000 + 625 Combine like terms: 250000 + 625 = 250625 625 + 50X + X2 = 250625 Factor a perfect square on the left side: (X + 25)(X + 25) = 250625 Calculate the square root of the right side: 500.624609863 Break this problem into two subproblems by setting (X + 25) equal to 500.624609863 and -500.624609863.Subproblem 1
X + 25 = 500.624609863 Simplifying X + 25 = 500.624609863 Reorder the terms: 25 + X = 500.624609863 Solving 25 + X = 500.624609863 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 = 500.624609863 + -25 Combine like terms: 25 + -25 = 0 0 + X = 500.624609863 + -25 X = 500.624609863 + -25 Combine like terms: 500.624609863 + -25 = 475.624609863 X = 475.624609863 Simplifying X = 475.624609863Subproblem 2
X + 25 = -500.624609863 Simplifying X + 25 = -500.624609863 Reorder the terms: 25 + X = -500.624609863 Solving 25 + X = -500.624609863 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 = -500.624609863 + -25 Combine like terms: 25 + -25 = 0 0 + X = -500.624609863 + -25 X = -500.624609863 + -25 Combine like terms: -500.624609863 + -25 = -525.624609863 X = -525.624609863 Simplifying X = -525.624609863Solution
The solution to the problem is based on the solutions from the subproblems. X = {475.624609863, -525.624609863}
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