Solve the quadratic equation by completing the square. 3x2 - 6x - 4 = 0

Answer:The solutions are[tex]x=1+\sqrt{\frac{7}{3}}[/tex][tex]x=1-\sqrt{\frac{7}{3}}[/tex]Step-by-step explanation:we have[tex]3x^{2}-6x-4=0[/tex]Group terms that contain the same variable, and move the constant to the opposite side of the equation[tex]3x^{2}-6x=4[/tex]Factor the leading coefficient [tex]3(x^{2}-2x)=4[/tex]Complete the square. Remember to balance the equation by adding the same constants to each side[tex]3(x^{2}-2x+1)=4+3[/tex][tex]3(x^{2}-2x+1)=7[/tex]Rewrite as perfect squares[tex]3(x-1)^{2}=7[/tex][tex](x-1)^{2}=\frac{7}{3}[/tex]square root both sides[tex]x-1=(+/-)\sqrt{\frac{7}{3}}[/tex][tex]x=1(+/-)\sqrt{\frac{7}{3}}[/tex][tex]x=1+\sqrt{\frac{7}{3}}[/tex][tex]x=1-\sqrt{\frac{7}{3}}[/tex]