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Simplifying x2 + 615x + -405000 = 0 Reorder the terms: -405000 + 615x + x2 = 0 Solving -405000 + 615x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '405000' to each side of the equation. -405000 + 615x + 405000 + x2 = 0 + 405000 Reorder the terms: -405000 + 405000 + 615x + x2 = 0 + 405000 Combine like terms: -405000 + 405000 = 0 0 + 615x + x2 = 0 + 405000 615x + x2 = 0 + 405000 Combine like terms: 0 + 405000 = 405000 615x + x2 = 405000 The x term is 615x. Take half its coefficient (307.5). Square it (94556.25) and add it to both sides. Add '94556.25' to each side of the equation. 615x + 94556.25 + x2 = 405000 + 94556.25 Reorder the terms: 94556.25 + 615x + x2 = 405000 + 94556.25 Combine like terms: 405000 + 94556.25 = 499556.25 94556.25 + 615x + x2 = 499556.25 Factor a perfect square on the left side: (x + 307.5)(x + 307.5) = 499556.25 Calculate the square root of the right side: 706.792932902 Break this problem into two subproblems by setting (x + 307.5) equal to 706.792932902 and -706.792932902.Subproblem 1
x + 307.5 = 706.792932902 Simplifying x + 307.5 = 706.792932902 Reorder the terms: 307.5 + x = 706.792932902 Solving 307.5 + x = 706.792932902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-307.5' to each side of the equation. 307.5 + -307.5 + x = 706.792932902 + -307.5 Combine like terms: 307.5 + -307.5 = 0.0 0.0 + x = 706.792932902 + -307.5 x = 706.792932902 + -307.5 Combine like terms: 706.792932902 + -307.5 = 399.292932902 x = 399.292932902 Simplifying x = 399.292932902Subproblem 2
x + 307.5 = -706.792932902 Simplifying x + 307.5 = -706.792932902 Reorder the terms: 307.5 + x = -706.792932902 Solving 307.5 + x = -706.792932902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-307.5' to each side of the equation. 307.5 + -307.5 + x = -706.792932902 + -307.5 Combine like terms: 307.5 + -307.5 = 0.0 0.0 + x = -706.792932902 + -307.5 x = -706.792932902 + -307.5 Combine like terms: -706.792932902 + -307.5 = -1014.292932902 x = -1014.292932902 Simplifying x = -1014.292932902Solution
The solution to the problem is based on the solutions from the subproblems. x = {399.292932902, -1014.292932902}
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