Solve x^2 - 6x - 2=0 giving your answer in simplified surd form.

SInce the question requires simplified surd form, it makes sense to use the quadratic formula immediately for this question.

This would give us

x = 6 [+-] squareroot(36-(4x1x-2)) / 2

which simplifies to

x= 6 [+-] squrt(44) / 2

look at the square root: is 44 divisible by a square number? Yes: 44=4x11

This means that we can make

squrt(44)=squrt(4x11)=squrt(4)xsqurt(11) = 2xsqurt(11)

Which turns our equation for x into:

x = 6 [+-] 2xsqurt(11) / 2

The numerator and denominator share a factor of 2 so

x = 3 [+-] squrt(11) which is in simplified surd form