find out the value of \( x: x^{\wedge} 2-1=0 \)

Step 1 ：\( x^{2} - 1 = 0 \)

Step 2 ：\( (x - 1)(x + 1) = 0 \)

Step 3 ：\( x - 1 = 0 \) or \( x + 1 = 0 \)