a^2 - 5a + 25 = 0 Using the quadratic formula, we get: a = (5 ± sqrt(5^2 - 4125)) / 2 = (5 ± sqrt(-75)) / 2
Since the square root of a negative number is not a real number, the equation has no real solutions. The roots of the original equation are also complex.
To solve this quadratic equation, we can let x = a to simplify the equation:
(a^4) - 10(a^3) + 250(a) - 625 = 0
Now, we can solve for a by factoring:
(a^4) - 10(a^3) + 250(a) - 625 = (a^2 - 5a + 25)(a^2 - 5a + 25) = 0
Now we can solve for a in each factor:
a^2 - 5a + 25 = 0
Using the quadratic formula, we get:
a = (5 ± sqrt(5^2 - 4125)) / 2 = (5 ± sqrt(-75)) / 2
Since the square root of a negative number is not a real number, the equation has no real solutions. The roots of the original equation are also complex.