we are given
[tex]x^2-12x+5=0[/tex]
we have to solve it by completing square method
step-1: Move 5 on right side
[tex]x^2-12x+5-5=0-5[/tex]
[tex]x^2-12x=-5[/tex]
step-2: Break middle term
[tex]x^2-2*6*x=-5[/tex]
step-3: Add 6^2 both sides
[tex]x^2-2*6*x+(6)^2=-5+(6)^2[/tex]
[tex](x-6)^2=31[/tex]
step-3: Solve for x
[tex]\sqrt{(x-6)^2} =\sqrt{31}[/tex]
we wil get two values
First value is
[tex]x-6=\sqrt{31}[/tex]
add both sides 6
[tex]x-6+6=6+\sqrt{31}[/tex]
[tex]x=6+\sqrt{31}[/tex]
Second value is
[tex]x-6=-\sqrt{31}[/tex]
add both sides 6
[tex]x-6+6=6-\sqrt{31}[/tex]
[tex]x=6-\sqrt{31}[/tex]
so, solutions are
[tex]x=6+\sqrt{31}[/tex]
[tex]x=6-\sqrt{31}[/tex].............Answer
