To solve the equation \( x^2 - 17x + 16 = 0 \), we can use the quadratic formula, which is given by:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
In this equation, the coefficients are:
- \( a = 1 \)
- \( b = -17 \)
- \( c = 16 \)
Now, we can calculate \( b^2 - 4ac \):
\[ b^2 - 4ac = (-17)^2 - 4(1)(16) = 289 - 64 = 225 \]
Now we can substitute \( b^2 - 4ac \) into the quadratic formula:
\[ x = \frac{17 \pm \sqrt{225}}{2 \cdot 1} = \frac{17 \pm 15}{2} \]
This gives us two solutions:
- \( x = \frac{17 + 15}{2} = \frac{32}{2} = 16 \)
- \( x = \frac{17 - 15}{2} = \frac{2}{2} = 1 \)
Thus, the solutions to the equation \( x^2 - 17x + 16 = 0 \) are:
\[ x = 16 \quad \text{and} \quad x = 1 \]