Solving Simple Quadratic Equations Practice

To solve the equation \( x^2 = 1625 \) by inspection, we take the square root of both sides.

The solutions are:
\[
x = \sqrt{1625} \quad \text{and} \quad x = -\sqrt{1625}
\]

Next, we need to simplify \(\sqrt{1625}\).

We can factor 1625:
\[
1625 = 25 \times 65 = 25 \times (5 \times 13) = 5^2 \times 5 \times 13
\]

Thus,
\[
\sqrt{1625} = \sqrt{25 \times 65} = \sqrt{25} \times \sqrt{65} = 5\sqrt{65}
\]

Therefore, the two real solutions to the equation \( x^2 = 1625 \) are:
\[
x = 5\sqrt{65} \quad \text{and} \quad x = -5\sqrt{65}
\]

Now we need to provide the solutions in the form requested, with the lesser number first:
\[
\{-5\sqrt{65}, 5\sqrt{65}\}
\]

So the answer is:
\(-5\sqrt{65}, 5\sqrt{65}\)