Question 163331
4x^2+6.4x+k=0  divide each term by 4
x^2+(6.4/4)x+k/4=0----eq1

Let (x+a)^2 be the solution to this quadratic
expand, using foil:
x^2+xa+xa+a^2=
x^2+2xa+a^2=0-------eq2
Now we know that eq2 has to be identical to eq1 in all respects, so:
2a=(6.4/4) divide each side by 2
a=(6.4/8)-------eq3
a^2=k/4-----------eq4

substitute eq3 into eq4
(6.4/8)^2=k/4 or
40.96/64=k/4   multiply each side by 4
k=40.96/16
CK
x^2+(6.4/4)x+(40.96/64)
(x+6.4/8)^2  expand using foil
x^2+(6.4/8)x+(6.4/8)x+(6.4/8)^2=
x^2+(6.4/4)x+40.96/64

We can work this problem without dividing each term by 4 as we did initially.
4x^2+6.4x+k----------------eq1a
Let (ax+b)^2 be the solution ( a perfect square) expand using foil
a^2x^2+abx+abx+b^2 or
a^2x^2+2abx+b^2-----again, this must be identical to eq1a, so:

a^2=4-------------eq2a


2ab=6.4-----------eq3a divide each side by 2a
b=6.4/2a-------substitute this into eq4a

and b^2=k-----eq4a
(6.4/2a)^2=k
(40.96/4a^2)=k  but from eq2a, a^2=4, therefore
k=(40.96/16)-------------------------same as before

Hope this helps---ptaylor