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Simplifying 500x + -25000 + -1x2 = 0 Reorder the terms: -25000 + 500x + -1x2 = 0 Solving -25000 + 500x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 25000 + -500x + x2 = 0 Move the constant term to the right: Add '-25000' to each side of the equation. 25000 + -500x + -25000 + x2 = 0 + -25000 Reorder the terms: 25000 + -25000 + -500x + x2 = 0 + -25000 Combine like terms: 25000 + -25000 = 0 0 + -500x + x2 = 0 + -25000 -500x + x2 = 0 + -25000 Combine like terms: 0 + -25000 = -25000 -500x + x2 = -25000 The x term is -500x. Take half its coefficient (-250). Square it (62500) and add it to both sides. Add '62500' to each side of the equation. -500x + 62500 + x2 = -25000 + 62500 Reorder the terms: 62500 + -500x + x2 = -25000 + 62500 Combine like terms: -25000 + 62500 = 37500 62500 + -500x + x2 = 37500 Factor a perfect square on the left side: (x + -250)(x + -250) = 37500 Calculate the square root of the right side: 193.64916731 Break this problem into two subproblems by setting (x + -250) equal to 193.64916731 and -193.64916731.Subproblem 1
x + -250 = 193.64916731 Simplifying x + -250 = 193.64916731 Reorder the terms: -250 + x = 193.64916731 Solving -250 + x = 193.64916731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + x = 193.64916731 + 250 Combine like terms: -250 + 250 = 0 0 + x = 193.64916731 + 250 x = 193.64916731 + 250 Combine like terms: 193.64916731 + 250 = 443.64916731 x = 443.64916731 Simplifying x = 443.64916731Subproblem 2
x + -250 = -193.64916731 Simplifying x + -250 = -193.64916731 Reorder the terms: -250 + x = -193.64916731 Solving -250 + x = -193.64916731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + x = -193.64916731 + 250 Combine like terms: -250 + 250 = 0 0 + x = -193.64916731 + 250 x = -193.64916731 + 250 Combine like terms: -193.64916731 + 250 = 56.35083269 x = 56.35083269 Simplifying x = 56.35083269Solution
The solution to the problem is based on the solutions from the subproblems. x = {443.64916731, 56.35083269}
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