To determine whether the values \( x = -1 \) and \( x = 73 \) are solutions to the quadratic equation \( 3x^2 - 4x - 4 = 3 \), we first rearrange the equation to the standard form:
\[ 3x^2 - 4x - 4 - 3 = 0 \]
This simplifies to:
\[ 3x^2 - 4x - 7 = 0 \]
We will now check if \( x = -1 \) and \( x = 73 \) satisfy this equation by substituting these values into the left side of the equation and checking if it equals zero.
- Checking \( x = -1 \):
\[ 3(-1)^2 - 4(-1) - 7 = 3(1) + 4 - 7 = 3 + 4 - 7 = 0 \]
Since the left side equals zero, \( x = -1 \) is a solution.
- Checking \( x = 73 \):
\[ 3(73)^2 - 4(73) - 7 \]
Calculating this step-by-step:
\[ 3(5329) - 292 - 7 = 15987 - 292 - 7 = 15987 - 299 = 15988 \]
Since \( 15988 \neq 0 \), \( x = 73 \) is not a solution.
Based on these evaluations, the correct conclusion is:
Only \( x = -1 \) is a solution.