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

Question

(
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 \({-9, \frac{3}{19}}\).