x^2 - 4x - 3 = 0
Using the quadratic formula, we have:
x = [4 +/- sqrt((-4)^2 - 4(1)(-3))] / [2(1)]
x = [4 +/- sqrt(16 + 12)] / 2
x = [4 +/- sqrt(28)] / 2
x = [4 +/- sqrt(4)sqrt(7)] / 2
x = [4 +/- 2sqrt(7)] / 2
x = 2 +/- sqrt(7)
x = 2 + sqrt(7) or x = 2 - sqrt(7)
Using completing the square:
x^2 - 4x - 3 = 0
(x^2 - 4x) - 3 = 0
(x - 2)^2 - 4 - 3 = 0
(x - 2)^2 - 7 = 0
(x - 2)^2 = 7
x - 2 = +/-sqrt(7)
x = 2 +/- sqrt(7)
x = 2 + sqrt(7) or x = 2 - sqrt(7)