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Simplifying x2 + 6x + -125 = 0 Reorder the terms: -125 + 6x + x2 = 0 Solving -125 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '125' to each side of the equation. -125 + 6x + 125 + x2 = 0 + 125 Reorder the terms: -125 + 125 + 6x + x2 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + 6x + x2 = 0 + 125 6x + x2 = 0 + 125 Combine like terms: 0 + 125 = 125 6x + x2 = 125 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 125 + 9 Reorder the terms: 9 + 6x + x2 = 125 + 9 Combine like terms: 125 + 9 = 134 9 + 6x + x2 = 134 Factor a perfect square on the left side: (x + 3)(x + 3) = 134 Calculate the square root of the right side: 11.575836903 Break this problem into two subproblems by setting (x + 3) equal to 11.575836903 and -11.575836903.Subproblem 1
x + 3 = 11.575836903 Simplifying x + 3 = 11.575836903 Reorder the terms: 3 + x = 11.575836903 Solving 3 + x = 11.575836903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 11.575836903 + -3 Combine like terms: 3 + -3 = 0 0 + x = 11.575836903 + -3 x = 11.575836903 + -3 Combine like terms: 11.575836903 + -3 = 8.575836903 x = 8.575836903 Simplifying x = 8.575836903Subproblem 2
x + 3 = -11.575836903 Simplifying x + 3 = -11.575836903 Reorder the terms: 3 + x = -11.575836903 Solving 3 + x = -11.575836903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -11.575836903 + -3 Combine like terms: 3 + -3 = 0 0 + x = -11.575836903 + -3 x = -11.575836903 + -3 Combine like terms: -11.575836903 + -3 = -14.575836903 x = -14.575836903 Simplifying x = -14.575836903Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.575836903, -14.575836903}
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