1 .Find the solutions to \(x^2 + 64 = 0.\)
2. Find all the solutions to \( x^2 - 6x + 13 = 0.\)
x^2 + 64 = 0
x^2 = -64 take both roots
x = ± √-64
x = ± 8i
x^2 - 6x + 13 = 0
x^2 - 6x = -13 complete the square on x
Take 1/2 of 6 = 3.....square it = 9 add to both sides
x^2 - 6x + 9 = -13 + 9 factor the left side, simplify the right
(x - 3)^2 = -4 take both roots
x - 3 ± √-4
x - 3 = ± 2i add 3 to both sides
x = ± 2i + 3