Question

Determine whether the values -1 and 3 are solutions to the quadratic equation
3x2 - 4x - 4 = 3. (1 point)
• Both x = - 1 and x = 3 are solutions.
• Neither x = -1 nor x = ] is a solution.
• Only x - 3 is a solution.
• Only x = - 1 is a solution.

Answer 1

To determine whether the values \( x = -1 \) and \( x = 3 \) are solutions to the quadratic equation \( 3x^2 - 4x - 4 = 3 \), we first simplify the equation:

1. Subtract 3 from both sides:
\[
3x^2 - 4x - 4 - 3 = 0
\]
This simplifies to:
\[
3x^2 - 4x - 7 = 0
\]

Next, we will substitute \( x = -1 \) and \( x = 3 \) into the simplified quadratic equation to see if either value satisfies it.

**For \( x = -1 \):**
\[
3(-1)^2 - 4(-1) - 7 = 3(1) + 4 - 7 = 3 + 4 - 7 = 0
\]
Thus, \( x = -1 \) is a solution.

**For \( x = 3 \):**
\[
3(3)^2 - 4(3) - 7 = 3(9) - 12 - 7 = 27 - 12 - 7 = 27 - 19 = 8
\]
Thus, \( x = 3 \) is not a solution.

In conclusion, the only solution is \( x = -1 \).

The answer is: **Only \( x = -1 \) is a solution.**