To determine whether \(-1\) and \(73\) are solutions to the quadratic equation \(3x^2 - 4x - 4 = 3\), we first rewrite the equation in standard form by moving all terms to one side:
\[ 3x^2 - 4x - 4 - 3 = 0 \]
This simplifies to:
\[ 3x^2 - 4x - 7 = 0 \]
Next, we will check if \(-1\) and \(73\) satisfy this equation by substituting each value into the left-hand side of the equation:
- Check if \(x = -1\) is a solution:
\[ 3(-1)^2 - 4(-1) - 7 \] \[ = 3(1) + 4 - 7 \] \[ = 3 + 4 - 7 \] \[ = 7 - 7 \] \[ = 0 \]
Since the left-hand side equals \(0\), \(-1\) is indeed a solution to the equation.
- Check if \(x = 73\) is a solution:
\[ 3(73)^2 - 4(73) - 7 \] First, calculate \(73^2\): \[ 73^2 = 5329 \]
Now substitute this value back into the equation:
\[ 3(5329) - 4(73) - 7 \] \[ = 15987 - 292 - 7 \] \[ = 15987 - 299 \] \[ = 15988 \]
Since the left-hand side does not equal \(0\), \(73\) is not a solution to the equation.
Conclusion:
- \(-1\) is a solution to the equation.
- \(73\) is not a solution to the equation.