x^2-(2m+1)x+m^2+5
=x^2-(2m+1)x+(2m+1)^2/4+m^2+5-(2m+1)^2/4
=[x-(2m+1)/2]^2+m^2+5-(2m+1)^2/4
x^2-(2m+1)x+m^2+5是完全平方式
即m^2+5-(2m+1)^2/4=0
m^2+5-(4m^2+4m+1)/4=0
4m^2+20-(4m^2+4m+1)=0
4m^2+20-4m^2-4m-1=0
20-4m-1=0
4m=19
m=19/4
x^2-(2m+1)x+m^2+5
=x^2-(2m+1)x+(2m+1)^2/4+m^2+5-(2m+1)^2/4
=[x-(2m+1)/2]^2+m^2+5-(2m+1)^2/4
x^2-(2m+1)x+m^2+5是完全平方式
即m^2+5-(2m+1)^2/4=0
m^2+5-(4m^2+4m+1)/4=0
4m^2+20-(4m^2+4m+1)=0
4m^2+20-4m^2-4m-1=0
20-4m-1=0
4m=19
m=19/4