16x2+8x+1=0

To solve the quadratic equation \( 16x^2 + 8x + 1 = 0 \), you can use the quadratic formula:

\[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \]

where \( a = 16 \), \( b = 8 \), and \( c = 1 \).

1. Calculate the discriminant (\( b^2 - 4ac \)):

\[ b^2 - 4ac = 8^2 - 4 \cdot 16 \cdot 1 = 64 - 64 = 0 \]

2. Since the discriminant is 0, there is one real solution (a double root).

3. Substitute the values into the quadratic formula:

\[ x = \frac{{-8 \pm \sqrt{0}}}{{2 \cdot 16}} = \frac{{-8}}{{32}} = -\frac{1}{4} \]

Thus, the solution to the equation \( 16x^2 + 8x + 1 = 0 \) is:

\[ x = -\frac{1}{4} \]