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Simplifying x2 + 25x + -260 = 0 Reorder the terms: -260 + 25x + x2 = 0 Solving -260 + 25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '260' to each side of the equation. -260 + 25x + 260 + x2 = 0 + 260 Reorder the terms: -260 + 260 + 25x + x2 = 0 + 260 Combine like terms: -260 + 260 = 0 0 + 25x + x2 = 0 + 260 25x + x2 = 0 + 260 Combine like terms: 0 + 260 = 260 25x + x2 = 260 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 = 260 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 260 + 156.25 Combine like terms: 260 + 156.25 = 416.25 156.25 + 25x + x2 = 416.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 416.25 Calculate the square root of the right side: 20.402205763 Break this problem into two subproblems by setting (x + 12.5) equal to 20.402205763 and -20.402205763.Subproblem 1
x + 12.5 = 20.402205763 Simplifying x + 12.5 = 20.402205763 Reorder the terms: 12.5 + x = 20.402205763 Solving 12.5 + x = 20.402205763 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 = 20.402205763 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 20.402205763 + -12.5 x = 20.402205763 + -12.5 Combine like terms: 20.402205763 + -12.5 = 7.902205763 x = 7.902205763 Simplifying x = 7.902205763Subproblem 2
x + 12.5 = -20.402205763 Simplifying x + 12.5 = -20.402205763 Reorder the terms: 12.5 + x = -20.402205763 Solving 12.5 + x = -20.402205763 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 = -20.402205763 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -20.402205763 + -12.5 x = -20.402205763 + -12.5 Combine like terms: -20.402205763 + -12.5 = -32.902205763 x = -32.902205763 Simplifying x = -32.902205763Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.902205763, -32.902205763}
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