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Simplifying x2 + 25x + -250 = -5 Reorder the terms: -250 + 25x + x2 = -5 Solving -250 + 25x + x2 = -5 Solving for variable 'x'. Reorder the terms: -250 + 5 + 25x + x2 = -5 + 5 Combine like terms: -250 + 5 = -245 -245 + 25x + x2 = -5 + 5 Combine like terms: -5 + 5 = 0 -245 + 25x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '245' to each side of the equation. -245 + 25x + 245 + x2 = 0 + 245 Reorder the terms: -245 + 245 + 25x + x2 = 0 + 245 Combine like terms: -245 + 245 = 0 0 + 25x + x2 = 0 + 245 25x + x2 = 0 + 245 Combine like terms: 0 + 245 = 245 25x + x2 = 245 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 = 245 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 245 + 156.25 Combine like terms: 245 + 156.25 = 401.25 156.25 + 25x + x2 = 401.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 401.25 Calculate the square root of the right side: 20.031225624 Break this problem into two subproblems by setting (x + 12.5) equal to 20.031225624 and -20.031225624.Subproblem 1
x + 12.5 = 20.031225624 Simplifying x + 12.5 = 20.031225624 Reorder the terms: 12.5 + x = 20.031225624 Solving 12.5 + x = 20.031225624 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 = 20.031225624 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 20.031225624 + -12.5 x = 20.031225624 + -12.5 Combine like terms: 20.031225624 + -12.5 = 7.531225624 x = 7.531225624 Simplifying x = 7.531225624Subproblem 2
x + 12.5 = -20.031225624 Simplifying x + 12.5 = -20.031225624 Reorder the terms: 12.5 + x = -20.031225624 Solving 12.5 + x = -20.031225624 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 = -20.031225624 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -20.031225624 + -12.5 x = -20.031225624 + -12.5 Combine like terms: -20.031225624 + -12.5 = -32.531225624 x = -32.531225624 Simplifying x = -32.531225624Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.531225624, -32.531225624}
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