To determine whether the values \(-1\) and \(73\) are solutions to the equation \(3x^2 - 4x - 4 = 3\), we need to check if substituting these values into the equation produces a true statement.
First, let's rewrite the equation:
\[ 3x^2 - 4x - 4 - 3 = 0 \] This simplifies to: \[ 3x^2 - 4x - 7 = 0 \]
Now, we will substitute \(x = -1\) into the equation:
\[ 3(-1)^2 - 4(-1) - 7 = 3(1) + 4 - 7 = 3 + 4 - 7 = 0 \]
Since this is true, \(x = -1\) is a solution.
Next, let's substitute \(x = 73\):
\[ 3(73)^2 - 4(73) - 7 = 3(5329) - 292 - 7 \] Calculating \(3(5329)\): \[ 3(5329) = 15987 \] Now we can substitute this back into the equation: \[ 15987 - 292 - 7 = 15987 - 299 = 15688 \neq 0 \]
Since substituting \(x = 73\) gives us a non-zero result, it means \(x = 73\) is not a solution.
Therefore, the correct conclusion is:
Only \(x = -1\) is a solution.