Question

Solve the factored quadratic equation (19x−3)(9+x)=0
. Enter the lesser number first. Use whole numbers or fractions for the answers.(2 points)
The solution set is {
,
}

Answer 1

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

1. Setting the first factor equal to zero:
\[
19x - 3 = 0
\]
\[
19x = 3
\]
\[
x = \frac{3}{19}
\]

2. Setting the second factor equal to zero:
\[
9 + x = 0
\]
\[
x = -9
\]

Now we have two solutions:
- \(x = \frac{3}{19}\)
- \(x = -9\)

The solution set, with the lesser number first, is:
\[
\{ -9, \frac{3}{19} \}
\]