Solve the equation. $$ 16 x^{2}-24 x+9=0 $$

Question

UpStudy AI · Accepted Answer

1. **Write down the quadratic equation:**

$$
   16x^2 - 24x + 9 = 0
   $$

2. **Compute the discriminant, $$ \Delta $$:**

$$
   \Delta = b^2 - 4ac = (-24)^2 - 4(16)(9) = 576 - 576 = 0
   $$

3. **Since $$ \Delta = 0 $$, the equation has one repeated solution. Use the quadratic formula:**

$$
   x = \frac{-b}{2a}
   $$

4. **Substitute the values:**

$$
   x = \frac{-(-24)}{2 \times 16} = \frac{24}{32} = \frac{3}{4}
   $$

5. **Final Answer:**

$$
   x = \frac{3}{4}
   $$
$$ x = \frac{3}{4} $$

Solve the equation.