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Simplifying x2 + 25x + -140000 = 0 Reorder the terms: -140000 + 25x + x2 = 0 Solving -140000 + 25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '140000' to each side of the equation. -140000 + 25x + 140000 + x2 = 0 + 140000 Reorder the terms: -140000 + 140000 + 25x + x2 = 0 + 140000 Combine like terms: -140000 + 140000 = 0 0 + 25x + x2 = 0 + 140000 25x + x2 = 0 + 140000 Combine like terms: 0 + 140000 = 140000 25x + x2 = 140000 The x term is 25x. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25x + 156.25 + x2 = 140000 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 140000 + 156.25 Combine like terms: 140000 + 156.25 = 140156.25 156.25 + 25x + x2 = 140156.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 140156.25 Calculate the square root of the right side: 374.374478297 Break this problem into two subproblems by setting (x + 12.5) equal to 374.374478297 and -374.374478297.Subproblem 1
x + 12.5 = 374.374478297 Simplifying x + 12.5 = 374.374478297 Reorder the terms: 12.5 + x = 374.374478297 Solving 12.5 + x = 374.374478297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 374.374478297 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 374.374478297 + -12.5 x = 374.374478297 + -12.5 Combine like terms: 374.374478297 + -12.5 = 361.874478297 x = 361.874478297 Simplifying x = 361.874478297Subproblem 2
x + 12.5 = -374.374478297 Simplifying x + 12.5 = -374.374478297 Reorder the terms: 12.5 + x = -374.374478297 Solving 12.5 + x = -374.374478297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -374.374478297 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -374.374478297 + -12.5 x = -374.374478297 + -12.5 Combine like terms: -374.374478297 + -12.5 = -386.874478297 x = -386.874478297 Simplifying x = -386.874478297Solution
The solution to the problem is based on the solutions from the subproblems. x = {361.874478297, -386.874478297}
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