To determine if \( x = -1 \) and \( x = 73 \) are solutions to the quadratic equation \( 3x^2 - 4x - 4 = 3 \), we first rewrite the equation in standard form by moving 3 to the left side:
\[ 3x^2 - 4x - 4 - 3 = 0 \implies 3x^2 - 4x - 7 = 0 \]
Next, we will substitute \( x = -1 \) and \( x = 73 \) into the equation to see if either yields a true statement.
Testing \( x = -1 \):
\[ 3(-1)^2 - 4(-1) - 7 = 0 \]
Calculating each term:
\[ 3(1) + 4 - 7 = 3 + 4 - 7 = 0 \]
This is true, so \( x = -1 \) is a solution.
Testing \( x = 73 \):
\[ 3(73)^2 - 4(73) - 7 = 0 \]
Calculating \( 73^2 \):
\[ 3(5329) - 292 - 7 = 0 \] \[ 15987 - 292 - 7 = 0 \] \[ 15987 - 299 = 0 \] \[ 15987 \neq 0 \]
This is not true, so \( x = 73 \) is not a solution.
Based on these results, we conclude:
Only \( x = -1 \) is a solution.