To solve the equation \( x^2 = 78 \) by inspection, we need to find two numbers whose squares equal 78.
The two real solutions can be found by taking the square root of both sides:
\[ x = \pm \sqrt{78} \]
We can simplify \( \sqrt{78} \):
\[ \sqrt{78} = \sqrt{39 \times 2} = \sqrt{39} \cdot \sqrt{2} \]
However, for our purposes, we can leave it in radical form.
The two real solutions are:
\[ x = -\sqrt{78} \quad \text{and} \quad x = \sqrt{78} \]
Since we need to enter the lesser number first, the final answer is:
\[ -\sqrt{78}, \sqrt{78} \]
If you prefer the numerical approximation:
\[ -\sqrt{78} \approx -8.83 \quad \text{and} \quad \sqrt{78} \approx 8.83 \]
So in exact form, the solutions remain:
\[ -\sqrt{78}, \sqrt{78} \]