Given -z = sqrt(-z+6)−z=√−z+6
Square both sides
color(white)("XXXX")XXXXz^2 = -z+6z2=−z+6
Re-arrange into standard form
color(white)("XXXX")XXXXz^2+z-6=0z2+z−6=0
Factor
color(white)("XXXX")XXXX(z+3)(z-2)=0(z+3)(z−2)=0
rArr⇒
color(white)("XXXX")XXXXz = -3 or z = +2z=−3orz=+2
Checking
color(white)("XXXX")XXXXwith z=-3z=−3
color(white)("XXXX")XXXXcolor(white)("XXXX")XXXX-z = sqrt(-z+6)−z=√−z+6
color(white)("XXXX")XXXXbecomes
color(white)("XXXX")XXXXcolor(white)("XXXX")XXXX3 = sqrt(3+6) = 33=√3+6=3
color(white)("XXXX")XXXXValid
color(white)("XXXX")XXXXwith z=2z=2
color(white)("XXXX")XXXXcolor(white)("XXXX")XXXX-z=sqrt(-z+6)−z=√−z+6
color(white)("XXXX")XXXXbecomes
color(white)("XXXX")XXXXcolor(white)("XXXX")XXXX-2 ?= sqrt(-2+6) = 2−2?=√−2+6=2
color(white)("XXXX")XXXXExtraneous