You can solve this by "completing the square." I find it easier to put the constant by itself on one side of the equal sign for that.

x^2 - 4x - 7 = 0

x^2 - 4x = 7 (add 7 to both sides)

x^2 - 4x + 4 = 7 + 4 (complete the square by adding (4/2)^2)

(x - 2)^2 = 11 (simplify)

x - 2 = ±√11 (square root both sides)

x^2 - 4x - 7 = 0

x^2 - 4x = 7 (add 7 to both sides)

x^2 - 4x + 4 = 7 + 4 (complete the square by adding (4/2)^2)

(x - 2)^2 = 11 (simplify)

x - 2 = ±√11 (square root both sides)

**x = 2 ± √11**(add 2 to both sides)