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Simplifying (X)(X) + -2X + -1 = 0 Multiply X * X X2 + -2X + -1 = 0 Reorder the terms: -1 + -2X + X2 = 0 Solving -1 + -2X + 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 + -2X + 1 + X2 = 0 + 1 Reorder the terms: -1 + 1 + -2X + X2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2X + X2 = 0 + 1 -2X + X2 = 0 + 1 Combine like terms: 0 + 1 = 1 -2X + X2 = 1 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 = 1 + 1 Reorder the terms: 1 + -2X + X2 = 1 + 1 Combine like terms: 1 + 1 = 2 1 + -2X + X2 = 2 Factor a perfect square on the left side: (X + -1)(X + -1) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (X + -1) equal to 1.414213562 and -1.414213562.Subproblem 1
X + -1 = 1.414213562 Simplifying X + -1 = 1.414213562 Reorder the terms: -1 + X = 1.414213562 Solving -1 + X = 1.414213562 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 = 1.414213562 + 1 Combine like terms: -1 + 1 = 0 0 + X = 1.414213562 + 1 X = 1.414213562 + 1 Combine like terms: 1.414213562 + 1 = 2.414213562 X = 2.414213562 Simplifying X = 2.414213562Subproblem 2
X + -1 = -1.414213562 Simplifying X + -1 = -1.414213562 Reorder the terms: -1 + X = -1.414213562 Solving -1 + X = -1.414213562 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 = -1.414213562 + 1 Combine like terms: -1 + 1 = 0 0 + X = -1.414213562 + 1 X = -1.414213562 + 1 Combine like terms: -1.414213562 + 1 = -0.414213562 X = -0.414213562 Simplifying X = -0.414213562Solution
The solution to the problem is based on the solutions from the subproblems. X = {2.414213562, -0.414213562}
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