x^2+10x+36 = (x+a)^2 +b

What is the value of a and b?

Question

x^2+10x+36 = (x+a)^2 +b

What is the value of a and b?

parthkohli · Answer

Simply complete the square in this case.

parthkohli · Answer

@ash2326 don't stop :)

ash2326 · Answer

@InspyR4D did you get the hint @ParthKohli gave?

anonymous · Answer

yup, thanks. I've completed the square but I don't know how to individually work out x, a or b

parthkohli · Answer

I wouldn't like to intimidate, but look at the following formula:$$ax^2 + bx + c \implies ax^2 + bx  - \left(b\over 2 \right)^2 + \left( b \over 2\right)^2 + c$$

parthkohli · Answer

It isn't too hard when you are working with it!$$x^2 + 10x + 36 \implies x^2 + 10x - \left(10 \over 2 \right)^2 + \left( 10 \over 2\right)^2 + c $$Or,$$x^2 + 10x - 5^2 + 5^2 + c$$

parthkohli · Answer

After that, we are left with the following:$$x^2 + 10x - 5^2 + 5^2 + 36$$We can simplify this by using the method stated below.$$x^2 + 10x + 25 - 25 + 36$$$$\implies x^2  + 10x + 25 + 11\qquad(-25 + 36 = +11)$$$$\implies (x + 5)^2 + 11$$