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Simplifying x2 + 10000x + 24993728 = 0 Reorder the terms: 24993728 + 10000x + x2 = 0 Solving 24993728 + 10000x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-24993728' to each side of the equation. 24993728 + 10000x + -24993728 + x2 = 0 + -24993728 Reorder the terms: 24993728 + -24993728 + 10000x + x2 = 0 + -24993728 Combine like terms: 24993728 + -24993728 = 0 0 + 10000x + x2 = 0 + -24993728 10000x + x2 = 0 + -24993728 Combine like terms: 0 + -24993728 = -24993728 10000x + x2 = -24993728 The x term is 10000x. Take half its coefficient (5000). Square it (25000000) and add it to both sides. Add '25000000' to each side of the equation. 10000x + 25000000 + x2 = -24993728 + 25000000 Reorder the terms: 25000000 + 10000x + x2 = -24993728 + 25000000 Combine like terms: -24993728 + 25000000 = 6272 25000000 + 10000x + x2 = 6272 Factor a perfect square on the left side: (x + 5000)(x + 5000) = 6272 Calculate the square root of the right side: 79.195959493 Break this problem into two subproblems by setting (x + 5000) equal to 79.195959493 and -79.195959493.Subproblem 1
x + 5000 = 79.195959493 Simplifying x + 5000 = 79.195959493 Reorder the terms: 5000 + x = 79.195959493 Solving 5000 + x = 79.195959493 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5000' to each side of the equation. 5000 + -5000 + x = 79.195959493 + -5000 Combine like terms: 5000 + -5000 = 0 0 + x = 79.195959493 + -5000 x = 79.195959493 + -5000 Combine like terms: 79.195959493 + -5000 = -4920.804040507 x = -4920.804040507 Simplifying x = -4920.804040507Subproblem 2
x + 5000 = -79.195959493 Simplifying x + 5000 = -79.195959493 Reorder the terms: 5000 + x = -79.195959493 Solving 5000 + x = -79.195959493 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5000' to each side of the equation. 5000 + -5000 + x = -79.195959493 + -5000 Combine like terms: 5000 + -5000 = 0 0 + x = -79.195959493 + -5000 x = -79.195959493 + -5000 Combine like terms: -79.195959493 + -5000 = -5079.195959493 x = -5079.195959493 Simplifying x = -5079.195959493Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4920.804040507, -5079.195959493}
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