Question

Solve the factored quadratic equation (19x−3)(9+x)=0 .(1 point) Responses 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={−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={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={−

Answer 1

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

Now, we have two solutions:
\[
x = \frac{3}{19} \quad \text{and} \quad x = -9
\]

Thus, the solution set is:
\[
x = \left\{ -9, \frac{3}{19} \right\}
\]

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