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Simplifying X2 + -2X + -133 = 0 Reorder the terms: -133 + -2X + X2 = 0 Solving -133 + -2X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '133' to each side of the equation. -133 + -2X + 133 + X2 = 0 + 133 Reorder the terms: -133 + 133 + -2X + X2 = 0 + 133 Combine like terms: -133 + 133 = 0 0 + -2X + X2 = 0 + 133 -2X + X2 = 0 + 133 Combine like terms: 0 + 133 = 133 -2X + X2 = 133 The X term is -2X. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2X + 1 + X2 = 133 + 1 Reorder the terms: 1 + -2X + X2 = 133 + 1 Combine like terms: 133 + 1 = 134 1 + -2X + X2 = 134 Factor a perfect square on the left side: (X + -1)(X + -1) = 134 Calculate the square root of the right side: 11.575836903 Break this problem into two subproblems by setting (X + -1) equal to 11.575836903 and -11.575836903.Subproblem 1
X + -1 = 11.575836903 Simplifying X + -1 = 11.575836903 Reorder the terms: -1 + X = 11.575836903 Solving -1 + X = 11.575836903 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + X = 11.575836903 + 1 Combine like terms: -1 + 1 = 0 0 + X = 11.575836903 + 1 X = 11.575836903 + 1 Combine like terms: 11.575836903 + 1 = 12.575836903 X = 12.575836903 Simplifying X = 12.575836903Subproblem 2
X + -1 = -11.575836903 Simplifying X + -1 = -11.575836903 Reorder the terms: -1 + X = -11.575836903 Solving -1 + X = -11.575836903 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + X = -11.575836903 + 1 Combine like terms: -1 + 1 = 0 0 + X = -11.575836903 + 1 X = -11.575836903 + 1 Combine like terms: -11.575836903 + 1 = -10.575836903 X = -10.575836903 Simplifying X = -10.575836903Solution
The solution to the problem is based on the solutions from the subproblems. X = {12.575836903, -10.575836903}
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