How do you express x^2+11x-15 in the form (x+a)^2+b

The answer is (x+11/2)^2-45 1/4 . Thanks in advance!

we call it completing the square.

x^2 + 11x - 15

you need the square of half of 11 to complete x^2 + 11x to a square. we need (11/2)^2

this number must be extracted from the 15. so we have

x^2 + 11x + (11/2)^2 - 15- (11/2)^2 =

(x + 11/2)^2 - (11/2)^2 - 15 =

(x + 11/2)^2 - 15 - 121/4 =

(x + 11/2)^2 - (181/4)

(x + 11/2)^2 - 45 1/4

x^2 + 11x - 15

x^2 + 11x + (11/2)^2 - (11/2)^2 - 15 =

(x + 11/2)^2 - (11/2)^2 - 15 =

(x + 11/2)^2 - 121/4 - 15 =

(x + 11/2)^2 - (30 1/4) - 15

(x + 11/2)^2 - 45 1/4