Question

How to solve 2x squared -6x-+=0

`{2x}^(2) - 6x - 1 = 0`

Answer 1

`2x^2-6x-1=0\ \ \ |:2\\\\x^2-3x-(1)/(2)=0\\\\x^2-2\cdot x\cdot(3)/(2)+\left((3)/(2)\right)^2-\left((3)/(2)\right)^2-(1)/(2)\\\\=\left(x-(3)/(2)\right)^2-(9)/(4)-(2)/(4)=0\\\\\left(x-(3)/(2)\right)^2-(11)/(4)=0\ \ \ \ |+(11)/(4)\\\\\left(x-(3)/(2)\right)^2=(11)/(4)\iff x-(3)/(2)=\pm\sqrt{(11)/(4)}\\\\x-(3)/(2)=-(√(11))/(2)\ \vee\ x-(3)/(2)=(√(11))/(2)\ \  \ \ |+(3)/(2)\\\\x=(3-√(11))/(2)\ \vee\ (3+√(11))/(2)`



`Used:\ (a-b)^2=a^2-2ab+b^2`