7. [0/1 Points] DETAILS MY NOTES Use the Square Root Property to solve the equation. \[ \begin{array}{l} x^{2}=-36 \\ x=6 \end{array} \]

The equation \( x^{2} = -36 \) indicates that we are looking for the square roots of a negative number. In the realm of real numbers, this is impossible because no real number squared will give a negative result. However, when we extend our understanding to complex numbers, we can find a solution! The square root of \(-36\) equals \(6i\) and \(-6i\), as \(i\) represents the imaginary unit where \(i^2 = -1\). In practice, the Square Root Property allows us to find solutions easily for any equation of the form \(x^2 = k\) by taking the square root of both sides, leading to \(x = \pm \sqrt{k}\). For real-world applications, complex numbers are frequently used in engineering, physics, and signal processing, where they help represent waves and oscillations, giving the power to analyze systems that would otherwise be challenging to solve within real numbers alone!