Question

Solve this quadratic equation using the quadratic formula. x^2 - 6x + 6 = 0

Answer 1

`x^2-6x+6=0\\\\a=1;\ b=-6;\ c=6\\\Delta=b^2-4ac\\\\\Delta=(-6)^2-4\cdot1\cdot6=36-24=12 \ \textgreater \ 0\\\\then\\x_1=(-b-\sqrt\Delta)/(2a)\ and\ x_2=(-b+\sqrt\Delta)/(2a)\\\\\sqrt\Delta=√(12)=√(4\cdot3)=\sqrt4\cdot\sqrt3=2\sqrt3\\\\x_1=(6-2\sqrt3)/(2\cdot1)=(6-2\sqrt3)/(2)=\boxed{3-\sqrt3}\\\\x_2=(6+2\sqrt3)/(2\cdot1)=(6+2\sqrt3)/(2)=\boxed{3+\sqrt3}`