Question 1112367
ONE WAY:
{{{(x+5)^2=x^2+10x+25}}} so options 2 and 4 will turn into {{{x^2+10x+something=0}}} ,
which cannot have the same solutions as
{{{x^2-10x*155=0}}} .
 
{{{(x-5)^2=x^2-10x+25}}} so options 2 and 4 will turn into {{{x^2-10x+something=0}}} ,
which would be the same equation,
and have the same solutions as
{{{x^2-10x-15=0}}} , when {{{something=-15}}} .
 
{{{(x-5)^2=5}}} <--> {{{x^2-10x+25=5}}} <--> {{{x^2-10x+25-5=0}}} <--> {{{x^2-10x+20=0}}}
does not have the same solutions as {{{x^2-10x-15=0}}} .
 
{{{(x-5)^2=40}}} <--> {{{x^2-10x+25=40}}} <--> {{{x^2-10x+25-40=0}}} <--> {{{x^2-10x-15=0}}}
is the same equation and has the same solutions as {{{x^2-10x-15=0}}} .
 
THE EXPECTED WAY FOR SHOW-YOUR-WORK QUESTIONS:
{{{x^2-10x-15=0}}}
{{{x^2-10x=15}}}
{{{x^2-10x+25=15+25}}}
{{{(x-5)^2=40}}}