write the quadratic expression x² - 16x - 6 in the form (x + a)² + b, we need to complete the square by adding and subtracting the square of half the x coefficient. The values of a and b are 8 and 58, respectively.
To write the quadratic expression x² - 16x - 6 in the form (x + a)² + b, we need to complete the square. First, let's group the terms
(x² - 16x) - 6
To complete the square, we take half of the coefficient of the x term (-16) and square it. This gives us (-16/2)² = 64. We add and subtract this value inside the parentheses:
(x² - 16x + 64) - 64 - 6
Now we can rewrite the expression as:
(x - 8)² + (64 - 6)
Simplifying further:
(x - 8)² + 58
Therefore, the values of a and b are 8 and 58, respectively.