if x^2+bx=(x+p)^2+q, express p and q in terms of b????

Question

campbell_st · Answer

expand the right hand side and collect like terms

$$x^2 + bx =  x^2 + 2px + p^2 + q$$

then 

$$bx = 2px + p^2 + q$$

equating coefficients

b = 2p and p^2 + q = 0

anonymous · Answer

my text gives the answer p=1/2b and q=-1/4b^2

jamesj · Answer

Are you sure you've given us the right equations then up top?  Because what campbell has written is correct. (btw, what he has written also implies that 
q = -4b^2)

jamesj · Answer

e.g., is it x^2 + x/b = .... ?

campbell_st · Answer

the question is simply about equation coefficients of like terms...all you need to do is expand and compare...

anonymous · Answer

attachment

anonymous · Answer

question 5

asnaseer · Answer

the answer that @campbell_st gave matches the answers given in your text book. just work through it, e.g.$$b=2p\implies p=\frac{1}{2}b$$
now just re-arrange$$p^2+q=0$$

campbell_st · Answer

well is b = 2p then p = b/2

and is p^2 + q = 0   and p = B/2

then (b/2)^2 + q = 0

q =- b^2/4

just make p and q the subjects

anonymous · Answer

thank you guys.

jamesj · Answer

Oh right.  I thought hc was saying p=1/2b and q=-1/4b^2, meaning p = 1/(2b), but no.

In which case, asnaseer is exactly right.