Question

Square root of the quantity x plus 7 end quantity minus 1 equals x

Answer 1

x = 2

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