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The quadratic x²−16x−6 can be written as (x-a)²+b. Find the values of a and b

User Jon Tan
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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.

User Mohamed Saligh
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