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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 by moving \(3\) to the left side:
\[
3x^2 - 4x - 4 - 3 = 0
\]
\[
3x^2 - 4x - 7 = 0
\]
Now we can substitute \(-1\) into the equation:
1. **Substituting \(x = -1\):**
\[
3(-1)^2 - 4(-1) - 7 = 0
\]
\[
3(1) + 4 - 7 = 0
\]
\[
3 + 4 - 7 = 0
\]
\[
0 = 0 \quad \text{(True)}
\]
Thus, \(-1\) is a solution to the equation.
2. **Substituting \(x = 73\):**
\[
3(73)^2 - 4(73) - 7 = 0
\]
Calculating \(73^2\):
\[
73^2 = 5329
\]
Now substitute:
\[
3(5329) - 4(73) - 7 = 0
\]
\[
15987 - 292 - 7 = 0
\]
Now perform the subtraction:
\[
15987 - 292 = 15695
\]
Then,
\[
15695 - 7 = 15688 \neq 0
\]
Thus, \(73\) is not a solution to the equation.
In conclusion:
- \(-1\) is a solution.
- \(73\) is not a solution.