Question

Solve the quadratic equation using square roots. (x - 4)^2 = 25

Answer 1

To solve the equation \((x - 4)^2 = 25\) using square roots, we start by taking the square root of both sides. This gives us:

\[
x - 4 = \pm 5
\]

Now we can split this into two separate equations to solve for \(x\):

1. \(x - 4 = 5\)
2. \(x - 4 = -5\)

**For the first equation:**

\[
x - 4 = 5
\]
Adding 4 to both sides, we get:

\[
x = 5 + 4 = 9
\]

**For the second equation:**

\[
x - 4 = -5
\]
Again, adding 4 to both sides, we have:

\[
x = -5 + 4 = -1
\]

Thus, the solutions to the equation \((x - 4)^2 = 25\) are:

\[
x = 9 \quad \text{and} \quad x = -1
\]

In conclusion, the final solutions are:

\(\boxed{9}\) and \(\boxed{-1}\)