Solving the Equation (x + 15)² = 54
This equation involves a square and requires us to use the square root to solve for x. Let's break down the steps:
1. Isolate the Squared Term

Begin by taking the square root of both sides of the equation. Remember that taking the square root can result in both positive and negative solutions.
√(x + 15)² = ±√54

This simplifies to:
x + 15 = ±√54
2. Simplify the Radical

Find the prime factorization of 54: 54 = 2 × 3 × 3 × 3 = 2 × 3² × 3.

We can take the square root of 3² which is 3:
x + 15 = ±√(2 × 3² × 3) = ±3√6
3. Isolate x

Subtract 15 from both sides of the equation:
x = 15 ± 3√6
4. The Solutions
Therefore, the solutions to the equation (x + 15)² = 54 are:
 x = 15 + 3√6
 x = 15  3√6
These are the exact solutions. You can approximate them using a calculator if needed.