Solve the following quations by using qardratic formula:
`256x^(2)-32x+1=0`

Answer

To solve the quadratic equation \( 256x^2 - 32x + 1 = 0 \) using the quadratic formula, we will follow these steps:

### Step 1: Identify coefficients
The standard form of a quadratic equation is \( ax^2 + bx + c = 0 \). Here, we identify:
- \( a = 256 \)
- \( b = -32 \)
- \( c = 1 \)

### Step 2: Write the quadratic formula
The quadratic formula is given by:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

### Step 3: Substitute the coefficients into the formula
Substituting the values of \( a \), \( b \), and \( c \) into the formula:
\[ x = \frac{-(-32) \pm \sqrt{(-32)^2 - 4 \cdot 256 \cdot 1}}{2 \cdot 256} \]

### Step 4: Simplify the expression
Calculating \( -(-32) \):
\[ x = \frac{32 \pm \sqrt{1024 - 1024}}{512} \]

### Step 5: Calculate the discriminant
Now, calculate the discriminant:
\[ 1024 - 1024 = 0 \]
Thus, we have:
\[ x = \frac{32 \pm \sqrt{0}}{512} \]

### Step 6: Simplify further
Since \( \sqrt{0} = 0 \):
\[ x = \frac{32}{512} \]

### Step 7: Reduce the fraction
Now, we simplify \( \frac{32}{512} \):
\[ x = \frac{1}{16} \]

### Conclusion
Thus, the solution to the quadratic equation \( 256x^2 - 32x + 1 = 0 \) is:
\[ x = \frac{1}{16} \]