2n=Pi*square root(2+n)

Question

solve for n, found answer online not sure how got to that answer

Answer 1

2n = pi sqrt(2 + n)  square everything

(2n)^2 = pi^2 (2 + n)   multiply the square

4n^2 = pi^2 (2 + n)

4n^2 = 2pi^2 +pi^2n

4n^2 -pi^2n - 2pi^2 = 0

4n^2 - 9.869n - 19.739 = 0

use quadratic equation

a = 4, b = -9.869, c = -19.739

[-(-9.869) +or- sqrt(-9.869^2 - 4 * 4 * (-19.739)] / 2 * 4

[9.869 +or- sqrt(97.397 + 315.824) / 8

[9.869 +or- sqrt(413.221)] / 8

(9.869 +or- 20.327) /8

30.196/8 or -1.307

 

Answer 2

Search me, Sir!