a $x^{2}-10 x+25=0$

Step 1 ：Given the quadratic equation: \(x^{2}-10x+25=0\)

Step 2 ：Use the quadratic formula: \(x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}\)

Step 3 ：Substitute the coefficients: a = 1, b = -10, and c = 25

Step 4 ：Calculate the discriminant: \(\Delta = b^{2} - 4ac = (-10)^{2} - 4(1)(25) = 100 - 100 = 0\)

Step 5 ：Substitute the discriminant and coefficients into the quadratic formula: \(x = \frac{-(-10) \pm \sqrt{0}}{2(1)}\)

Step 6 ：\(x = \frac{10 \pm 0}{2}\)

Step 7 ：\(\boxed{x = 5}\)