Question

Please solve equations by completing square

Answer 1

$x^2-4x+1=0\\ x^2-4x+4-3=0\\ (x-2)^2=3\\ |x-2|=\sqrt3\\ x-2=\sqrt3 \vee x-2=-\sqrt3\\ x=2+\sqrt3 \vee x=2-\sqrt3$

$x^2+6x-9=0\\ x^2+6x+9-18=0\\ (x+3)^2=18\\ |x+3|=\sqrt{18}=3\sqrt2\\ x+3=3\sqrt2 \vee x+3=-3\sqrt2\\ x=-3+3\sqrt2 \vee x=-3-3\sqrt2$

$x^2+20x+3=0\\ x^2+20x+100-97=0\\ (x+10)^2=97\\ |x+10|=\sqrt{97}\\ x+10=\sqrt{97} \vee x+10=-\sqrt{97}\\ x=-10+\sqrt{97} \vee x=-10-\sqrt{97}$

$x^2-2x-5=0\\ x^2-2x+1-6=0\\ (x-1)^2=6\\ |x-1|=\sqrt6\\ x-1=\sqrt6 \vee x-1=-\sqrt6\\ x=1+\sqrt6 \vee x=1-\sqrt6$