Problem: solve (x+3)^2=-13
is answer the empty set no solution
(x + 3)^2 = -13
(x + 3) * (x + 3) = -13
x^2 + 3x + 3x + 9 = -13
x^2 + 6x + 9 = -13
x^2 + 6x + 9 + 13 = -13 + 13
x^2 + 6x + 22 = 0
-b ± sqrt(b^2 - 4*a*c)
x = -----------------------------
2a
-6 ± sqrt(6^2 - 4*1*22)
x = -----------------------------
2(1)
-6 ± sqrt(36 - 88)
x = ----------------------
2
-6 ± sqrt(-52)
x = -----------------
2
The discriminant, sqrt(-52), means that
the solution involves imaginary numbers.