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Simplifying x2 + -100000x + 3000000 = 0 Reorder the terms: 3000000 + -100000x + x2 = 0 Solving 3000000 + -100000x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-3000000' to each side of the equation. 3000000 + -100000x + -3000000 + x2 = 0 + -3000000 Reorder the terms: 3000000 + -3000000 + -100000x + x2 = 0 + -3000000 Combine like terms: 3000000 + -3000000 = 0 0 + -100000x + x2 = 0 + -3000000 -100000x + x2 = 0 + -3000000 Combine like terms: 0 + -3000000 = -3000000 -100000x + x2 = -3000000 The x term is -100000x. Take half its coefficient (-50000). Square it (2500000000) and add it to both sides. Add '2500000000' to each side of the equation. -100000x + 2500000000 + x2 = -3000000 + 2500000000 Reorder the terms: 2500000000 + -100000x + x2 = -3000000 + 2500000000 Combine like terms: -3000000 + 2500000000 = 2497000000 2500000000 + -100000x + x2 = 2497000000 Factor a perfect square on the left side: (x + -50000)(x + -50000) = 2497000000 Calculate the square root of the right side: 49969.990994596 Break this problem into two subproblems by setting (x + -50000) equal to 49969.990994596 and -49969.990994596.Subproblem 1
x + -50000 = 49969.990994596 Simplifying x + -50000 = 49969.990994596 Reorder the terms: -50000 + x = 49969.990994596 Solving -50000 + x = 49969.990994596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50000' to each side of the equation. -50000 + 50000 + x = 49969.990994596 + 50000 Combine like terms: -50000 + 50000 = 0 0 + x = 49969.990994596 + 50000 x = 49969.990994596 + 50000 Combine like terms: 49969.990994596 + 50000 = 99969.990994596 x = 99969.990994596 Simplifying x = 99969.990994596Subproblem 2
x + -50000 = -49969.990994596 Simplifying x + -50000 = -49969.990994596 Reorder the terms: -50000 + x = -49969.990994596 Solving -50000 + x = -49969.990994596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50000' to each side of the equation. -50000 + 50000 + x = -49969.990994596 + 50000 Combine like terms: -50000 + 50000 = 0 0 + x = -49969.990994596 + 50000 x = -49969.990994596 + 50000 Combine like terms: -49969.990994596 + 50000 = 30.009005404 x = 30.009005404 Simplifying x = 30.009005404Solution
The solution to the problem is based on the solutions from the subproblems. x = {99969.990994596, 30.009005404}
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