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

Question

Responses

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.

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

Both x=−1 and x=73 are solutions.

Answer 1

To determine whether the values −1 and 73 are solutions to the equation \( 3x^2 - 4x - 4 = 3 \), we will first rewrite the equation in standard form:

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

Simplifying this gives:

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

Next, we'll substitute \( x = -1 \) and \( x = 73 \) into the equation to check each one.

1. Checking \( x = -1 \):

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

Since the left side equals the right side (0), \( x = -1 \) is a solution.

2. Checking \( x = 73 \):

\[ 3(73)^2 - 4(73) - 7 = 3(5329) - 292 - 7 \] Calculating \( 3(5329) \):

\[ 3 \times 5329 = 15987 \] Now calculate:

\[ 15987 - 292 - 7 = 15987 - 299 = 15688 \]

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

Thus, the conclusion is that only \( x = -1 \) is a solution.

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