Question

Solve the equation. X^2-6x+6=0

Answer 1

`x^2-6x+6=0\\ x^2-6x+9-3=0\\ (x-3)^2=3\\ x-3=\sqrt 3 \vee x-3=-\sqrt3\\ x=3+\sqrt3 \vee x=3-\sqrt3`

Answer 2

`x^2-6x+6=0 \\ \\a=1, \ \ b=-6, \ \ c=6 \\\\\Delta =b^2-4ac = (-6)^2 -4\cdot1\cdot 6 = 36-24=12\\\\√(\Delta )=√(12)=√(4\cdot 3)=2√(3)\\ \\x_(1)=(-b-√(\Delta) )/(2a)=(6-2√(3))/(2 )=(2( 3- √(3)))/(2)= 3- √(3)\\\\x_(2)=(-b+√(\Delta) )/(2a)=(6+2√(3))/(2 )=(2( 3+ √(3)))/(2)= 3+ √(3)`