Question

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

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.

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

Both x=−1
and x=73
are solutions.
Both x equals negative 1 and x equals Start Fraction 7 over 3 End Fraction are solutions.

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

Answer 1

To determine if \( x = -1 \) and \( x = 73 \) are solutions to the quadratic equation \( 3x^2 - 4x - 4 = 3 \), we first rewrite the equation in standard form by moving 3 to the left side:

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

Next, we will substitute \( x = -1 \) and \( x = 73 \) into the equation to see if either yields a true statement.

**Testing \( x = -1 \):**

\[
3(-1)^2 - 4(-1) - 7 = 0
\]

Calculating each term:

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

This is true, so \( x = -1 \) is a solution.

**Testing \( x = 73 \):**

\[
3(73)^2 - 4(73) - 7 = 0
\]

Calculating \( 73^2 \):

\[
3(5329) - 292 - 7 = 0
\]
\[
15987 - 292 - 7 = 0
\]
\[
15987 - 299 = 0
\]
\[
15987 \neq 0
\]

This is not true, so \( x = 73 \) is not a solution.

Based on these results, we conclude:

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