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Simplifying x2 + -900x + -202500 = 0 Reorder the terms: -202500 + -900x + x2 = 0 Solving -202500 + -900x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '202500' to each side of the equation. -202500 + -900x + 202500 + x2 = 0 + 202500 Reorder the terms: -202500 + 202500 + -900x + x2 = 0 + 202500 Combine like terms: -202500 + 202500 = 0 0 + -900x + x2 = 0 + 202500 -900x + x2 = 0 + 202500 Combine like terms: 0 + 202500 = 202500 -900x + x2 = 202500 The x term is -900x. Take half its coefficient (-450). Square it (202500) and add it to both sides. Add '202500' to each side of the equation. -900x + 202500 + x2 = 202500 + 202500 Reorder the terms: 202500 + -900x + x2 = 202500 + 202500 Combine like terms: 202500 + 202500 = 405000 202500 + -900x + x2 = 405000 Factor a perfect square on the left side: (x + -450)(x + -450) = 405000 Calculate the square root of the right side: 636.396103068 Break this problem into two subproblems by setting (x + -450) equal to 636.396103068 and -636.396103068.Subproblem 1
x + -450 = 636.396103068 Simplifying x + -450 = 636.396103068 Reorder the terms: -450 + x = 636.396103068 Solving -450 + x = 636.396103068 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '450' to each side of the equation. -450 + 450 + x = 636.396103068 + 450 Combine like terms: -450 + 450 = 0 0 + x = 636.396103068 + 450 x = 636.396103068 + 450 Combine like terms: 636.396103068 + 450 = 1086.396103068 x = 1086.396103068 Simplifying x = 1086.396103068Subproblem 2
x + -450 = -636.396103068 Simplifying x + -450 = -636.396103068 Reorder the terms: -450 + x = -636.396103068 Solving -450 + x = -636.396103068 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '450' to each side of the equation. -450 + 450 + x = -636.396103068 + 450 Combine like terms: -450 + 450 = 0 0 + x = -636.396103068 + 450 x = -636.396103068 + 450 Combine like terms: -636.396103068 + 450 = -186.396103068 x = -186.396103068 Simplifying x = -186.396103068Solution
The solution to the problem is based on the solutions from the subproblems. x = {1086.396103068, -186.396103068}
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