Answer:
The solutions are [tex]x=2(+/-)\sqrt{11}[/tex]
Step-by-step explanation:
we have
[tex]x^{2}-4x-7=0[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]x^{2}-4x=7[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex]x^{2}-4x+4=7+4[/tex]
[tex]x^{2}-4x+4=11[/tex]
Rewrite as perfect squares
[tex](x-2)^{2}=11[/tex]
Take square root both sides
[tex]x-2=(+/-)\sqrt{11}[/tex]
[tex]x=2(+/-)\sqrt{11}[/tex]
