Given a and b unit vectors, if |a+b|=sqrt3, determine (2a-5b) . (b+3a)

Just wanted to know if someone could check if I have the correct solution and answer to the q above.

-13a.b+6|a|^2-5|b|^2

=-13(0.5)+6(1)^2-5(1)^2

=-5.5

I got 0.5 above for a.b dot product like this:

|a+b|=sqrt3^2

|a+b|^2=(a+b)(a+b)

3=(a^2)+2a.b+b^2

0.5=a.b