Answer:
x = 2±sqrt(11)
Explanation:
x^2 -4x - 7 =0
Add 7 to each side
x^2 -4x -7+7 =0+7
x^2 -4x =7
To complete the square take the coefficient of the x term and divide by 2 and then square it. Add it to both sides
-4 /2 = -2 then square
(-2)^2 = 4
Add 4 to both sides
x^2 -4x+4 =7+4
x^2 -4x+4 = 11
Factor the left side into (x-b/2)^2
(x-2)^2 =11
Take the square root of each side
sqrt((x-2)^2) =±sqrt(11)
x-2 = ±sqrt(11)
Add to to each side
x-2+2 = 2±sqrt(11)
x = 2±sqrt(11)