Question

Determine whether the values −1
and 73
are solutions to the quadratic equation 3x2−4x−4=3
.(1 point)
Responses

Only x=−1
is a solution.
Only x equals negative 1 is a solution.

Only x=73
is a solution.
Only x equals Start Fraction 7 over 3 End Fraction is a solution.

Neither x=−1
nor x=73
is a solution.
Neither x equals negative 1 nor x equals Start Fraction 7 over 3 End Fraction is a solution.

Both x=−1
and x=73
are solutions.

Answer 1

To determine whether the values \( x = -1 \) and \( x = 73 \) are solutions to the quadratic equation \( 3x^2 - 4x - 4 = 3 \), we first rewrite the equation in standard form by subtracting 3 from both sides:

\[
3x^2 - 4x - 4 - 3 = 0
\]
\[
3x^2 - 4x - 7 = 0
\]

Now we can check each value separately by substituting them into the equation \( 3x^2 - 4x - 7 \) and seeing if the result equals zero.

**1. Check \( x = -1 \):**

\[
3(-1)^2 - 4(-1) - 7
\]

Calculating this step-by-step:

\[
3(1) + 4 - 7 = 3 + 4 - 7 = 0
\]

So, \( x = -1 \) is a solution.

**2. Check \( x = 73 \):**

\[
3(73)^2 - 4(73) - 7
\]

Calculating this step-by-step:

\[
3(5329) - 292 - 7 = 15987 - 292 - 7 = 15987 - 299 = 15688
\]

Since \( 15688 \neq 0 \), \( x = 73 \) is not a solution.

Based on our checks:

- \( x = -1 \) is a solution.
- \( x = 73 \) is not a solution.

Thus the correct response is:

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