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
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