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Simplifying 2x2 + -5x + -1000 = 0 Reorder the terms: -1000 + -5x + 2x2 = 0 Solving -1000 + -5x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -500 + -2.5x + x2 = 0 Move the constant term to the right: Add '500' to each side of the equation. -500 + -2.5x + 500 + x2 = 0 + 500 Reorder the terms: -500 + 500 + -2.5x + x2 = 0 + 500 Combine like terms: -500 + 500 = 0 0 + -2.5x + x2 = 0 + 500 -2.5x + x2 = 0 + 500 Combine like terms: 0 + 500 = 500 -2.5x + x2 = 500 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 500 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 500 + 1.5625 Combine like terms: 500 + 1.5625 = 501.5625 1.5625 + -2.5x + x2 = 501.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 501.5625 Calculate the square root of the right side: 22.395591084 Break this problem into two subproblems by setting (x + -1.25) equal to 22.395591084 and -22.395591084.Subproblem 1
x + -1.25 = 22.395591084 Simplifying x + -1.25 = 22.395591084 Reorder the terms: -1.25 + x = 22.395591084 Solving -1.25 + x = 22.395591084 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 22.395591084 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 22.395591084 + 1.25 x = 22.395591084 + 1.25 Combine like terms: 22.395591084 + 1.25 = 23.645591084 x = 23.645591084 Simplifying x = 23.645591084Subproblem 2
x + -1.25 = -22.395591084 Simplifying x + -1.25 = -22.395591084 Reorder the terms: -1.25 + x = -22.395591084 Solving -1.25 + x = -22.395591084 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -22.395591084 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -22.395591084 + 1.25 x = -22.395591084 + 1.25 Combine like terms: -22.395591084 + 1.25 = -21.145591084 x = -21.145591084 Simplifying x = -21.145591084Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.645591084, -21.145591084}
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