To solve the equation #x^2+10x+16=0# using the completing square method, as coefficient of #x^2# is #1# and independent term #16# positive, we have to identify factors of #16# whose sum is #10#, coefficient of #x# term.

These are #2# and #8# and hence we should split the equation as follows:

#x^2+2x+8x+16=0# or #x(x+2)+8(x+2)=0# i.e.

#(x+2)(x+8)=0#.

Hence either #x+2=0# i.e. #x=-2# or

#x+8=0# i.e. #x=-8#

[In general if equation is in form #ax^2+bx+c=0#, one should identify two factors whose product is #a*c# and sum is #b#.]