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Simplifying x2 + 8000x + -2500000 = 0 Reorder the terms: -2500000 + 8000x + x2 = 0 Solving -2500000 + 8000x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2500000' to each side of the equation. -2500000 + 8000x + 2500000 + x2 = 0 + 2500000 Reorder the terms: -2500000 + 2500000 + 8000x + x2 = 0 + 2500000 Combine like terms: -2500000 + 2500000 = 0 0 + 8000x + x2 = 0 + 2500000 8000x + x2 = 0 + 2500000 Combine like terms: 0 + 2500000 = 2500000 8000x + x2 = 2500000 The x term is 8000x. Take half its coefficient (4000). Square it (16000000) and add it to both sides. Add '16000000' to each side of the equation. 8000x + 16000000 + x2 = 2500000 + 16000000 Reorder the terms: 16000000 + 8000x + x2 = 2500000 + 16000000 Combine like terms: 2500000 + 16000000 = 18500000 16000000 + 8000x + x2 = 18500000 Factor a perfect square on the left side: (x + 4000)(x + 4000) = 18500000 Calculate the square root of the right side: 4301.162633521 Break this problem into two subproblems by setting (x + 4000) equal to 4301.162633521 and -4301.162633521.Subproblem 1
x + 4000 = 4301.162633521 Simplifying x + 4000 = 4301.162633521 Reorder the terms: 4000 + x = 4301.162633521 Solving 4000 + x = 4301.162633521 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4000' to each side of the equation. 4000 + -4000 + x = 4301.162633521 + -4000 Combine like terms: 4000 + -4000 = 0 0 + x = 4301.162633521 + -4000 x = 4301.162633521 + -4000 Combine like terms: 4301.162633521 + -4000 = 301.162633521 x = 301.162633521 Simplifying x = 301.162633521Subproblem 2
x + 4000 = -4301.162633521 Simplifying x + 4000 = -4301.162633521 Reorder the terms: 4000 + x = -4301.162633521 Solving 4000 + x = -4301.162633521 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4000' to each side of the equation. 4000 + -4000 + x = -4301.162633521 + -4000 Combine like terms: 4000 + -4000 = 0 0 + x = -4301.162633521 + -4000 x = -4301.162633521 + -4000 Combine like terms: -4301.162633521 + -4000 = -8301.162633521 x = -8301.162633521 Simplifying x = -8301.162633521Solution
The solution to the problem is based on the solutions from the subproblems. x = {301.162633521, -8301.162633521}
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