What are the x-intercepts of the circle (x - 3) 2 + (y - 4) 2 = 24?

(x-3) 2 + (y-4) 2=24

2x-6+2y=24

2x-14+2y=24

2x=24+14-2y

2x=38-2y

x=19-y

X-intercept ⇒ When y = 0

(x - 3) ² + (y - 4) ² = 24

When y = 0,

(x - 3) ² + (0 - 4) ² = 24

(x - 3) ² + 16 = 24

(x - 3) ² = 8

(x - 3) = ±√8

x = √8 + 3 or x = - √8 + 3

x = (3 + 2√2) or (3 - 2√2) [Radical Form]

x = 5.83 or 0.17 [Decimal Form]

Answer: (5.83, 0) and (0.17, 0)