Final answer:
The quadratic equation p^2 + 35 = 10p has two complex solutions.
Step-by-step explanation:
To find the complex solutions for the equation p^2 + 35 = 10p, we can first rewrite it as p^2 - 10p + 35 = 0.
This is a quadratic equation in the form ax^2 + bx + c = 0, where a = 1, b = -10, and c = 35.
To solve the quadratic equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the values, we get:
p = (10 ± √((-10)^2 - 4(1)(35))) / (2(1))
Now calculating, we have:
p = (10 ± √(100 - 140)) / 2
p = (10 ± √(-40)) / 2
Since taking the square root of a negative number results in a complex solution, the quadratic equation has two complex solutions.