How many solutions would the equation x^2 = -9 have? You do not need to solve for x

1 answer

The equation \( x^2 = -9 \) does not have any real solutions because the square of any real number is non-negative, meaning it cannot equal a negative number like \(-9\).

However, in the context of complex numbers, we can find solutions. Taking the square root of both sides would yield \( x = \pm 3i \), where \( i \) is the imaginary unit (defined by \( i^2 = -1 \)).

In total, the equation \( x^2 = -9 \) has 2 complex solutions: \( 3i \) and \( -3i \).