Question

Find the solutions

(x-3)^2 = 49

Answer 1

To solve the equation \((x - 3)^2 = 49\), we can start by taking the square root of both sides.

1. Take the square root:
\[
x - 3 = \pm 7
\]

This gives us two equations to solve:

2. **First equation:**
\[
x - 3 = 7
\]
Adding 3 to both sides:
\[
x = 10
\]

3. **Second equation:**
\[
x - 3 = -7
\]
Again, adding 3 to both sides:
\[
x = -4
\]

So, the solutions to the equation \((x - 3)^2 = 49\) are:
\[
\boxed{10} \quad \text{and} \quad \boxed{-4}
\]