Determine whether the values −1

Question

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.

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.
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 whether the values \( x = -1 \) and \( x = 73 \) are solutions to the quadratic equation \( 3x^2 - 4x - 4 = 3 \), we first rewrite the equation:

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

Now we will test both values, \( x = -1 \) and \( x = 73 \), in the equation \( 3x^2 - 4x - 7 = 0 \).

Testing \( x = -1 \):

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

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

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Testing \( x = 73 \):

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

Calculating \( 3(5329) \):

\[ 3 \times 5329 = 15987 \]

Now, substituting back into the equation:

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

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

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Thus, the final conclusion is:

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