To solve the quadratic equation \(1x^2 - 8x + 16 = 0\) using the quadratic formula, we can identify the coefficients:
- \(a = 1\)
- \(b = -8\)
- \(c = 16\)
The quadratic formula is given by:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
First, calculate the discriminant (\(b^2 - 4ac\)):
\[ b^2 = (-8)^2 = 64 \] \[ 4ac = 4 \cdot 1 \cdot 16 = 64 \] \[ b^2 - 4ac = 64 - 64 = 0 \]
Since the discriminant is 0, there will be one real solution (a repeated root):
Now substitute the values into the quadratic formula:
\[ x = \frac{-(-8) \pm \sqrt{0}}{2 \cdot 1} \] \[ x = \frac{8 \pm 0}{2} \] \[ x = \frac{8}{2} = 4 \]
Thus, the equation \(1x^2 - 8x + 16 = 0\) has one repeated solution:
\[ \boxed{4} \]