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Simplifying 0 = x2 + -2500x + -202500 Reorder the terms: 0 = -202500 + -2500x + x2 Solving 0 = -202500 + -2500x + x2 Solving for variable 'x'. Combine like terms: 0 + 202500 = 202500 202500 + 2500x + -1x2 = -202500 + -2500x + x2 + 202500 + 2500x + -1x2 Reorder the terms: 202500 + 2500x + -1x2 = -202500 + 202500 + -2500x + 2500x + x2 + -1x2 Combine like terms: -202500 + 202500 = 0 202500 + 2500x + -1x2 = 0 + -2500x + 2500x + x2 + -1x2 202500 + 2500x + -1x2 = -2500x + 2500x + x2 + -1x2 Combine like terms: -2500x + 2500x = 0 202500 + 2500x + -1x2 = 0 + x2 + -1x2 202500 + 2500x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 202500 + 2500x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -202500 + -2500x + x2 = 0 Move the constant term to the right: Add '202500' to each side of the equation. -202500 + -2500x + 202500 + x2 = 0 + 202500 Reorder the terms: -202500 + 202500 + -2500x + x2 = 0 + 202500 Combine like terms: -202500 + 202500 = 0 0 + -2500x + x2 = 0 + 202500 -2500x + x2 = 0 + 202500 Combine like terms: 0 + 202500 = 202500 -2500x + x2 = 202500 The x term is -2500x. Take half its coefficient (-1250). Square it (1562500) and add it to both sides. Add '1562500' to each side of the equation. -2500x + 1562500 + x2 = 202500 + 1562500 Reorder the terms: 1562500 + -2500x + x2 = 202500 + 1562500 Combine like terms: 202500 + 1562500 = 1765000 1562500 + -2500x + x2 = 1765000 Factor a perfect square on the left side: (x + -1250)(x + -1250) = 1765000 Calculate the square root of the right side: 1328.533025559 Break this problem into two subproblems by setting (x + -1250) equal to 1328.533025559 and -1328.533025559.Subproblem 1
x + -1250 = 1328.533025559 Simplifying x + -1250 = 1328.533025559 Reorder the terms: -1250 + x = 1328.533025559 Solving -1250 + x = 1328.533025559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1250' to each side of the equation. -1250 + 1250 + x = 1328.533025559 + 1250 Combine like terms: -1250 + 1250 = 0 0 + x = 1328.533025559 + 1250 x = 1328.533025559 + 1250 Combine like terms: 1328.533025559 + 1250 = 2578.533025559 x = 2578.533025559 Simplifying x = 2578.533025559Subproblem 2
x + -1250 = -1328.533025559 Simplifying x + -1250 = -1328.533025559 Reorder the terms: -1250 + x = -1328.533025559 Solving -1250 + x = -1328.533025559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1250' to each side of the equation. -1250 + 1250 + x = -1328.533025559 + 1250 Combine like terms: -1250 + 1250 = 0 0 + x = -1328.533025559 + 1250 x = -1328.533025559 + 1250 Combine like terms: -1328.533025559 + 1250 = -78.533025559 x = -78.533025559 Simplifying x = -78.533025559Solution
The solution to the problem is based on the solutions from the subproblems. x = {2578.533025559, -78.533025559}
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