Final answer:
The equation x² - 16x - 6 can be written in the form (x - a)² + b by completing the square, which results in the values of a being 8 and b being -70.
Step-by-step explanation:
The student's question involves completing the square for the quadratic equation x² - 16x - 6 to write it in the form of (x-a)² + b.
To complete the square, the coefficient of x should be halved and then squaring that half. We have:
- The coefficient of x is -16.
- Halve -16 to get -8.
- Square -8 to get 64.
Add and subtract this square inside the quadratic:
- x² - 16x + 64 - 64 - 6
- This can be written as (x - 8)² - 70.
Now the equation is in the desired form, where a is 8 and b is -70.