To determine if the values \(−1\) and \(73\) are solutions to the quadratic equation \(3x^2−4x−4=3\), we first need to rearrange the equation into standard form. We subtract \(3\) from both sides:
\[ 3x^2 - 4x - 4 - 3 = 0 \] \[ 3x^2 - 4x - 7 = 0 \]
Now we can evaluate whether \(x = -1\) and \(x = 73\) are solutions by substituting these values into the equation.
- Checking \(x = -1\):
\[ 3(-1)^2 - 4(-1) - 7 = 3(1) + 4 - 7 = 3 + 4 - 7 = 0 \]
So \(x = -1\) is indeed a solution.
- Checking \(x = 73\):
\[ 3(73)^2 - 4(73) - 7 \]
Calculating \(3(73^2) = 3(5329) = 15987\),
Calculating \(-4(73) = -292\),
Now, substituting these values in:
\[ 15987 - 292 - 7 = 15987 - 299 = 15688 \]
Since \(15688 \neq 0\), \(x = 73\) is not a solution.
From these evaluations, we conclude:
- \(x = -1\) is a solution.
- \(x = 73\) is not a solution.
Thus, the correct response is: Only \(x = -1\) is a solution.