Question

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

−
3
)
(
9
+

)
=
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 can find the values of \(x\) by setting each factor equal to zero.

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

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

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

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

So, the solution set is \(\{-9, \frac{3}{19}\}\).