Question

Use the quadratic formula to solve. Express your answer in simplest form.
25, n, squared, minus, 15, n, plus, 4, equals, 5, n
25n
2
−15n+4=
5n

Answer 1

Start with 25n^2 − 15n + 4 = 5n. Move all terms to one side:
25n^2 − 20n + 4 = 0.

Use the quadratic formula n = [−b ± sqrt(b^2 − 4ac)]/(2a) with a = 25, b = −20, c = 4:
n = [20 ± sqrt((−20)^2 − 4·25·4)]/(2·25)
= [20 ± sqrt(400 − 400)]/50
= [20 ± 0]/50
= 20/50
= 2/5.

So the solution (double root) is n = 2/5.