Answer:
x = 2
Step-by-step explanation:
√(x + 7) − 1 = x
√(x + 7) = x + 1
x + 7 = (x + 1)²
x + 7 = x² + 2x + 1
0 = x² + x − 6
0 = (x + 3) (x − 2)
x = -3 or 2
Check for extraneous solutions:
√(-3 + 7) − 1 = -3
√4 − 1 = -3
2 − 1 = -3
1 = -3
x ≠ -3
√(2 + 7) − 1 = 2
√9 − 1 = 2
3 − 1 = 2
2 = 2
x = 2
