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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:
\[
\boxed{4}
\]