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This gives two potential solutions:

\[ t = \frac{-3 + 282.8}{2} \approx 139.9 \]

\[ t = \frac{-3 - 282.8}{2} \approx -142.9 \]

Since time cannot be negative, the valid solution is:

\(\boxed{139.9}\)

A programmer is optimizing a neural network and models the loss function as \( L(x) = 2x^2 - 8x + k \). Find \( k \) if the minimum loss occurs at \( x = 2 \) and the loss there is 4.

The vertex form of a quadratic function \( ax^2 + bx + c \) occurs at \( x = -\frac{b}{2a} \). For \( L(x) = 2x^2 - 8x + k \),

\[ a = 2, \, b = -8 \]

\[ x_{vertex} = -\frac{-8}{2 \times 2} = 2 \]

The minimum loss occurs at \( x = 2 \), and \( L(2) = 4 \). Substitute \( x = 2 \) into \( L(x) \):

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