Find the x-intercepts of the graph of the function: (y-6) = (x+5) ^2

-¹/₃ (y - 6) = (x + 5) ²

-¹/₃ (0 - 6) = (x + 5) (x + 5)

-¹/₃ (-6) = (x (x + 5) + 5 (x + 5))

2 = (x (x) + x (5) + 5 (x) + 5 (5))

2 = x² + 5x + 5x + 25

2 = x² + 10x + 25

- 2 - 2

0 = x² + 10x + 23

x = - (10) ± √ ((10) ² - 4 (1) (23))

2 (1)

x = - 10 ± √ (100 - 92)

2

x = - 10 ± √ (8)

2

x = - 10 ± 2√ (2)

2

x = - 5 ± √ (2)

x = - 5 + √ (2) U x = - 5 - √ (2)

The x-intercepts of the graph of the function is - 5 ± √ (2).