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Simplifying x2 + 25x + 1 = 0 Reorder the terms: 1 + 25x + x2 = 0 Solving 1 + 25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 25x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 25x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 25x + x2 = 0 + -1 25x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 25x + x2 = -1 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 = -1 + 156.25 Reorder the terms: 156.25 + 25x + x2 = -1 + 156.25 Combine like terms: -1 + 156.25 = 155.25 156.25 + 25x + x2 = 155.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 155.25 Calculate the square root of the right side: 12.459935794 Break this problem into two subproblems by setting (x + 12.5) equal to 12.459935794 and -12.459935794.Subproblem 1
x + 12.5 = 12.459935794 Simplifying x + 12.5 = 12.459935794 Reorder the terms: 12.5 + x = 12.459935794 Solving 12.5 + x = 12.459935794 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 = 12.459935794 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 12.459935794 + -12.5 x = 12.459935794 + -12.5 Combine like terms: 12.459935794 + -12.5 = -0.040064206 x = -0.040064206 Simplifying x = -0.040064206Subproblem 2
x + 12.5 = -12.459935794 Simplifying x + 12.5 = -12.459935794 Reorder the terms: 12.5 + x = -12.459935794 Solving 12.5 + x = -12.459935794 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 = -12.459935794 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -12.459935794 + -12.5 x = -12.459935794 + -12.5 Combine like terms: -12.459935794 + -12.5 = -24.959935794 x = -24.959935794 Simplifying x = -24.959935794Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.040064206, -24.959935794}
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