Please answer I need help

Question

find all angles,0 less than it equal to θ< 360, that satisfy the equation below, to the nearest 10th of a degree.

-2 tan² θ - 4 tan θ + 2 = 3 tan θ + 5

Answer 1

-2 tan² θ - 4 tan θ + 2 = 3 tan θ + 5

-2 tan² θ - 7 tab θ - 3 = 0

2 tan² θ + 7 tan θ + 3 = 0

(2 tan θ + 1)(tan θ + 3) = 0

Can you solve for θ and answer?

Answer 2

-2tan²(θ) - 4tan(θ) + 2 = 3tan(θ) + 5

-2tan²(θ) - 4tan(θ) - 3tan(θ) + 2 - 5 = 0

-2tan²(θ) - 7tan(θ) - 3 = 0

Let x = tan(θ), then: -2tan²(θ) - 7tan(θ) - 3 = 0 becomes:

-2x² - 7x - 3 = 0

2x² + 7x + 3 = 0

(x + 3)(2x + 1) = 0

x = -3

x = -1/2

Replace x with tan(θ) to get

tan(θ) = -3 or θ = tan^-1(-3)

tan(θ) = -1/2 or θ = tan^-1(-1/2)

Using a calculator, tan^-1(-3) = -71.6° this angle does not meet the requirements of being between 0 and 360. The equivalent angle would be 360° - 71.6° = 288.4°. However, the angle 180° from this will also have a tangent of -3. So 288.4° - 180° = 108.4°

Using a calculator, tan^-1(-1/2) = -26.6° this angle does not meet the requirements of being between 0 and 360. The equivalent angle would be 360° - 26.6° = 333.4°. However, the angle 180° from this will also have a tangent of -1/2. So 333.4° - 180° = 153.4°

The solutions then are θ = 108.4°, 153.4°, 288.4°, and 333.4°