Question

how to solve 2x squared -6x-+=0
${2x}^{2} - 6x - 1 = 0$

Answer 1

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


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