- Solve the quadratic equation using the squa \[ 9=(x+8)^{2} \]

To solve the equation \( 9 = (x+8)^2 \), start by taking the square root of both sides. This gives you \( \pm 3 = x + 8 \). You’ll then separate the two cases: For the positive case: \( x + 8 = 3 \) leading to \( x = -5 \). For the negative case: \( x + 8 = -3 \) leading to \( x = -11 \). Thus, the two solutions are \( x = -5 \) and \( x = -11 \). Now, let's wrap our heads around this! Quadratic equations like this one pop up everywhere from physics to engineering, as they model things like projectile motion. Understanding the square root step helps when you’re in real-life situations needing quick calculations—like figuring out the max height of a thrown ball or the cost to build a fence around a garden! When solving quadratics, one common mistake is forgetting to consider the plus and minus from taking the square root. Always remember those two scenarios! Also, double-check your work by plugging your solutions back into the original equation to ensure both satisfy it. It's like a mini celebration whenever your numbers click back together!