Solve the quadratic equation using completing the square. \[ p^{2}-4 p=45 \]

To solve the quadratic equation \( p^{2}-4 p=45 \) by completing the square, we first rearrange the equation: \[ p^2 - 4p - 45 = 0. \] Next, we focus on the left side to complete the square. Take the coefficient of \( p \), which is \(-4\), halve it to get \(-2\), and then square it, yielding \(4\). We add \(4\) and subtract \(4\) on the left side: \[ p^2 - 4p + 4 - 4 - 45 = 0, \] \[ (p - 2)^2 - 49 = 0. \] Now, we can rewrite the equation: \[ (p - 2)^2 = 49. \] Taking the square root of both sides gives us: \[ p - 2 = 7 \quad \text{or} \quad p - 2 = -7. \] Now, solving for \( p \): 1. \( p - 2 = 7 \) leads to \( p = 9 \). 2. \( p - 2 = -7 \) leads to \( p = -5 \). Thus, the solutions to the equation are: \[ p = 9 \quad \text{and} \quad p = -5. \]