Question 484772
{{{sqrt(2x)=x-4}}}
{{{(sqrt(2x))^2=(x-4)^2}}}
{{{2x=x^2-8x+16}}}
{{{x^2-8x+16-2x=0}}}
{{{x^2-10x+16=0}}}
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{x = (-(-10) +- sqrt((-10)^2-4*1*16 ))/(2*1) }}}
{{{x = (10+- sqrt(36))/2 }}}
{{{x [1]= (10- 6)/2 =2}}}
{{{x [2]= (10+ 6)/2 =8}}}
In equations, like this, we have to check answer
Check {{{x[1]=2}}} {{{sqrt(2*2)=2-4}}}
{{{sqrt(4)=-2}}}
{{{2=-2}}} incorrect, then {{{x[1]=2}}} exterior root
Check {{{x[2]=8}}} {{{sqrt(2*8)=8-4}}}
{{{sqrt(16)=4}}}
{{{4=4}}}correct
Answer x=8