Explanation:
For a quadratic equation ax² + bx + c = 0, x can be found with the quadratic formula:
x = [ -b ± √(b² − 4ac) ] / 2a
-x² − x + 1 = 0
Here, a = -1, b = -1, and c = 1.
x = [ -(-1) ± √((-1)² − 4(-1)(1)) ] / 2(-1)
x = [ 1 ± √(1 + 4) ] / -2
x = (1 ± √5) / -2
x = (-1 ± √5) / 2
The two values of x are (-1 − √5) / 2 and (-1 + √5) / 2.