Question

Solve the factored quadratic equation (19x−3)(9+x)=0(1 point)ResponsesThe solution set is x={−9,193}The solution set is x is equal to negative 9 comma 19 thirdsThe solution set is x={−9,319}The solution set is x is equal to negative 9 comma 3 over 19The solution set is x={−9,3}The solution set is x is equal to negative 9 comma 3The solution set is x={193,9}

Answer 1

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

1. \(19x - 3 = 0\)
2. \(9 + x = 0\)

**Solving the first equation:**

\[
19x - 3 = 0 \implies 19x = 3 \implies x = \frac{3}{19}
\]

**Solving the second equation:**

\[
9 + x = 0 \implies x = -9
\]

So the solutions to the equation are:

\[
x = -9 \quad \text{and} \quad x = \frac{3}{19}
\]

The solution set is:

\[
x = \{-9, \frac{3}{19}\}
\]

Therefore, the correct response is:

**The solution set is \(x\) is equal to negative 9 comma \(3\) over \(19\).**