Answer:
(x+8)^2 - 67
Explanation:
1) Rearrange the quadratic into the standard format: ax^2 + bx + c
In this case you rearrange it to x^2 + 16x - 3
2) Write out the initial bracket: (x + b/2)^2 - Just divide the value of b (which in this case is 16) by 2 (which in this case gives you 8)
3) Multiply out the brackets and compare to the original to find what you need to add or subtract to complete the square
In this case you do (x+8)^2 which gives you x^2 + 16x +64
You compare this to the original: x^2 + 16x - 3
4) Add or Subtract the adjusting number to make it match the original
In this case you need to subtract 67 from x^2 + 16x +64 (which is the same as (x+8)^2) in order to make it match the original x^2 + 16x - 3
64 - 67 = -3