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Simplifying X2 + 950X + 202500 = 0 Reorder the terms: 202500 + 950X + X2 = 0 Solving 202500 + 950X + 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 + 950X + -202500 + X2 = 0 + -202500 Reorder the terms: 202500 + -202500 + 950X + X2 = 0 + -202500 Combine like terms: 202500 + -202500 = 0 0 + 950X + X2 = 0 + -202500 950X + X2 = 0 + -202500 Combine like terms: 0 + -202500 = -202500 950X + X2 = -202500 The X term is 950X. Take half its coefficient (475). Square it (225625) and add it to both sides. Add '225625' to each side of the equation. 950X + 225625 + X2 = -202500 + 225625 Reorder the terms: 225625 + 950X + X2 = -202500 + 225625 Combine like terms: -202500 + 225625 = 23125 225625 + 950X + X2 = 23125 Factor a perfect square on the left side: (X + 475)(X + 475) = 23125 Calculate the square root of the right side: 152.069063257 Break this problem into two subproblems by setting (X + 475) equal to 152.069063257 and -152.069063257.Subproblem 1
X + 475 = 152.069063257 Simplifying X + 475 = 152.069063257 Reorder the terms: 475 + X = 152.069063257 Solving 475 + X = 152.069063257 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-475' to each side of the equation. 475 + -475 + X = 152.069063257 + -475 Combine like terms: 475 + -475 = 0 0 + X = 152.069063257 + -475 X = 152.069063257 + -475 Combine like terms: 152.069063257 + -475 = -322.930936743 X = -322.930936743 Simplifying X = -322.930936743Subproblem 2
X + 475 = -152.069063257 Simplifying X + 475 = -152.069063257 Reorder the terms: 475 + X = -152.069063257 Solving 475 + X = -152.069063257 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-475' to each side of the equation. 475 + -475 + X = -152.069063257 + -475 Combine like terms: 475 + -475 = 0 0 + X = -152.069063257 + -475 X = -152.069063257 + -475 Combine like terms: -152.069063257 + -475 = -627.069063257 X = -627.069063257 Simplifying X = -627.069063257Solution
The solution to the problem is based on the solutions from the subproblems. X = {-322.930936743, -627.069063257}
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