Solve the equation algebraically, and then find the values on the interval [0, 2π). (Enter your answers as a comma-separated list. Round to four decimal places.) tan^2(x) + 7 tan(x) − 7 = 0

Answer 1

tan^2(x) + 7 tan(x) − 7 = 0

Complete the square to solve:

Tan²(x) + 7Tan(x) = 7

7/2 = 3.5

Tan²(x) + 7Tan(x) + 3.5² = 7 + 3.5²

(Tan(x) + 3.5)² = 19.25

Tan(x) + 3.5 = √19.25 = ±4.387

Tan(x) = 0.875 and -7.887

x = Tan^-1(0.875) = 41.588° and -82.774°