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Simplifying X2 + (x + -1)(x + -1) = 1 Reorder the terms: X2 + (-1 + x)(x + -1) = 1 Reorder the terms: X2 + (-1 + x)(-1 + x) = 1 Multiply (-1 + x) * (-1 + x) X2 + (-1(-1 + x) + x(-1 + x)) = 1 X2 + ((-1 * -1 + x * -1) + x(-1 + x)) = 1 X2 + ((1 + -1x) + x(-1 + x)) = 1 X2 + (1 + -1x + (-1 * x + x * x)) = 1 X2 + (1 + -1x + (-1x + x2)) = 1 Combine like terms: -1x + -1x = -2x X2 + (1 + -2x + x2) = 1 Reorder the terms: 1 + X2 + -2x + x2 = 1 Add '-1' to each side of the equation. 1 + X2 + -2x + -1 + x2 = 1 + -1 Reorder the terms: 1 + -1 + X2 + -2x + x2 = 1 + -1 Combine like terms: 1 + -1 = 0 0 + X2 + -2x + x2 = 1 + -1 X2 + -2x + x2 = 1 + -1 Combine like terms: 1 + -1 = 0 X2 + -2x + x2 = 0 Solving X2 + -2x + x2 = 0 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '2x' to each side of the equation. X2 + -2x + 2x + x2 = 0 + 2x Combine like terms: -2x + 2x = 0 X2 + 0 + x2 = 0 + 2x X2 + x2 = 0 + 2x Remove the zero: X2 + x2 = 2x Add '-1x2' to each side of the equation. X2 + x2 + -1x2 = 2x + -1x2 Combine like terms: x2 + -1x2 = 0 X2 + 0 = 2x + -1x2 X2 = 2x + -1x2 Simplifying X2 = 2x + -1x2 Reorder the terms: X2 + -2x + x2 = 2x + -2x + -1x2 + x2 Combine like terms: 2x + -2x = 0 X2 + -2x + x2 = 0 + -1x2 + x2 X2 + -2x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 X2 + -2x + x2 = 0 Factor a trinomial. (X + -1x)(X + -1x) = 0Subproblem 1
Set the factor '(X + -1x)' equal to zero and attempt to solve: Simplifying X + -1x = 0 Solving X + -1x = 0 Move all terms containing X to the left, all other terms to the right. Add 'x' to each side of the equation. X + -1x + x = 0 + x Combine like terms: -1x + x = 0 X + 0 = 0 + x X = 0 + x Remove the zero: X = x Simplifying X = xSubproblem 2
Set the factor '(X + -1x)' equal to zero and attempt to solve: Simplifying X + -1x = 0 Solving X + -1x = 0 Move all terms containing X to the left, all other terms to the right. Add 'x' to each side of the equation. X + -1x + x = 0 + x Combine like terms: -1x + x = 0 X + 0 = 0 + x X = 0 + x Remove the zero: X = x Simplifying X = xSolution
X = {x, x}
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