X2-20x3+64=0

It looks like you have a polynomial equation:

\[ x^2 - 20x + 64 = 0 \]

To solve this quadratic equation, you can use the quadratic formula:

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

In your equation, the coefficients are:

• \( a = 1 \)
• \( b = -20 \)
• \( c = 64 \)

Now, plug these values into the quadratic formula:

1. Calculate the discriminant (\( b^2 - 4ac \)): \[ b^2 - 4ac = (-20)^2 - 4(1)(64) = 400 - 256 = 144 \]

2. Now, substitute the values into the formula: \[ x = \frac{-(-20) \pm \sqrt{144}}{2(1)} = \frac{20 \pm 12}{2} \]

3. This gives us two potential solutions:

   • First solution: \[ x = \frac{20 + 12}{2} = \frac{32}{2} = 16 \]
   • Second solution: \[ x = \frac{20 - 12}{2} = \frac{8}{2} = 4 \]

Thus, the solutions to the equation \( x^2 - 20x + 64 = 0 \) are:

\[ x = 16 \quad \text{and} \quad x = 4 \]