f(x)= x^2 -6x +21
0 =x^2-6x+21
subtract 21 from each side to prepare for completing the square
-21 = x^2 -6x
completing the square (b/2)^2
(-6/2) ^ =3^2 = 9
add 9 to each side
-21 +9 = x^2 - 6x + 9
-21 +9 =(x-3) ^2
-12 = (x-3)^2
take the square root of each side
+- sqrt(-12) = x-3
add 3 to each side, take out the negative inside the square root
3 +- i sqrt(12)=x
simplify the square root sqrt(12)= sqrt(4)sqrt(3) =2sqrt(3)
3 +- i 2sqrt (3) = x
Answer: 3+2isqrt(3)
3-2isqrt(3)
