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The best way to factor this is to use the quadratic equation.
Using an equation of the form:
ax2 + bx + c = 0
You use the quadratic formula like this:
x = [-b +(or -) sqrt(b2-4ac)]/2a
For your problem, a = 2, b = -6, and c = 9. Therefore:
x = [6 +(or -) sqrt(36 - 4(2)(9))]/4 = [6 +(or -) sqrt(36-72)]/4
= [6 +(or -) sqrt(-36)]/4 = (6 +(or -)6i)/4 = 3/2 +(or -)3i/2
Therefore the factorization is (x - 3/2 - 3i/2)(x - 3/2 + 3i/2).
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