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Simplifying -1x2 + 800x + -2500 = 0 Reorder the terms: -2500 + 800x + -1x2 = 0 Solving -2500 + 800x + -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'. 2500 + -800x + x2 = 0 Move the constant term to the right: Add '-2500' to each side of the equation. 2500 + -800x + -2500 + x2 = 0 + -2500 Reorder the terms: 2500 + -2500 + -800x + x2 = 0 + -2500 Combine like terms: 2500 + -2500 = 0 0 + -800x + x2 = 0 + -2500 -800x + x2 = 0 + -2500 Combine like terms: 0 + -2500 = -2500 -800x + x2 = -2500 The x term is -800x. Take half its coefficient (-400). Square it (160000) and add it to both sides. Add '160000' to each side of the equation. -800x + 160000 + x2 = -2500 + 160000 Reorder the terms: 160000 + -800x + x2 = -2500 + 160000 Combine like terms: -2500 + 160000 = 157500 160000 + -800x + x2 = 157500 Factor a perfect square on the left side: (x + -400)(x + -400) = 157500 Calculate the square root of the right side: 396.86269666 Break this problem into two subproblems by setting (x + -400) equal to 396.86269666 and -396.86269666.Subproblem 1
x + -400 = 396.86269666 Simplifying x + -400 = 396.86269666 Reorder the terms: -400 + x = 396.86269666 Solving -400 + x = 396.86269666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '400' to each side of the equation. -400 + 400 + x = 396.86269666 + 400 Combine like terms: -400 + 400 = 0 0 + x = 396.86269666 + 400 x = 396.86269666 + 400 Combine like terms: 396.86269666 + 400 = 796.86269666 x = 796.86269666 Simplifying x = 796.86269666Subproblem 2
x + -400 = -396.86269666 Simplifying x + -400 = -396.86269666 Reorder the terms: -400 + x = -396.86269666 Solving -400 + x = -396.86269666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '400' to each side of the equation. -400 + 400 + x = -396.86269666 + 400 Combine like terms: -400 + 400 = 0 0 + x = -396.86269666 + 400 x = -396.86269666 + 400 Combine like terms: -396.86269666 + 400 = 3.13730334 x = 3.13730334 Simplifying x = 3.13730334Solution
The solution to the problem is based on the solutions from the subproblems. x = {796.86269666, 3.13730334}
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