Question

Solve the factored quadratic equation (13x + 3) (9x - 14) = 0.

The solution set is x = {-13/3,9/14}.
The solution set is x = {-3,14}.
The solution set is x = {-3/13, 9/14}.
The solution set is x = {-3/13,1 5/9}.

Answer 1

To solve the factored quadratic equation \((13x + 3)(9x - 14) = 0\), we can set each factor to zero and solve for \(x\):

1. **First factor:**
\(13x + 3 = 0\)
Subtract 3 from both sides:
\(13x = -3\)
Now, divide by 13:
\(x = -\frac{3}{13}\)

2. **Second factor:**
\(9x - 14 = 0\)
Add 14 to both sides:
\(9x = 14\)
Now, divide by 9:
\(x = \frac{14}{9}\)

Now, we can compile the solutions together:
The solution set is \(x = \left\{-\frac{3}{13}, \frac{14}{9}\right\}\).

Thus, the correct solution from the options provided is:
**The solution set is \(x = \left\{-\frac{3}{13}, \frac{14}{9}\right\}\)**.