Solve the factored quadratic equation (19x−3)(9+x)=0

.(1 point)
Responses

The solution set is x={−9,319}
.
The solution set is x equals left brace negative 9 comma Start Fraction 3 over 19 End Fraction right brace .

The solution set is x={−9,193}
.
The solution set is x equals left brace negative 9 comma Start Fraction 19 over 3 End Fraction right brace .

The solution set is x={193,9}
.
The solution set is x equals left brace Start Fraction 19 over 3 End Fraction comma 9 right brace .

The solution set is x={−9,3}
.

1 answer

To solve the factored quadratic equation \((19x - 3)(9 + x) = 0\), we can set each factor to zero:

  1. Set the first factor to zero: \[ 19x - 3 = 0 \] Solving for \(x\): \[ 19x = 3 \implies x = \frac{3}{19} \]

  2. Set the second factor to zero: \[ 9 + x = 0 \] Solving for \(x\): \[ x = -9 \]

Thus, the solutions are: \[ x = -9 \quad \text{and} \quad x = \frac{3}{19} \]

The solution set is: \[ x = { -9, \frac{3}{19} } \]

So the correct response is: The solution set is \( x = { -9, \frac{3}{19} } \).

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