To find the value of \( a \) in the expression \( a^2 + 6.2^2 + 3.8^2 \), we first evaluate \( 6.2^2 \) and \( 3.8^2 \):
\[ 6.2^2 = 38.44 \]
\[ 3.8^2 = 14.44 \]
Next, we add these two values together:
\[ 38.44 + 14.44 = 52.88 \]
Now, the equation becomes:
\[ a^2 + 52.88 = 0 \]
To solve for \( a^2 \):
\[ a^2 = -52.88 \]
Since \( a^2 \) is negative, there is no real solution for \( a \). Instead, we can express it in terms of imaginary numbers:
\[ a = \pm \sqrt{-52.88} = \pm i \sqrt{52.88} \]
Calculating \( \sqrt{52.88} \):
\[ \sqrt{52.88} \approx 7.27 \]
Thus, the solutions for \( a \) are:
\[ a \approx \pm 7.27i \]
So, the solution in terms of imaginary numbers is:
\[ a = \pm 7.27i \]