What is the general solution for 8cos^2(x)+14cos(x)=-3 ?

The general solution for 8cos^2(x)+14cos(x)=-3 is x=1.82347…+2pin,x=-1.82347…+2pin

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8cos^2(x)+14cos(x)=-3

8 cos^{2} (x) + 14 cos (x) = - 3

x = 1.82347 \dots + 2 πn, x = - 1.82347 \dots + 2 πn

Solution steps

8 cos^{2} (x) + 14 cos (x) = - 3

Solve by substitution

cos (x) = - \frac{1}{4}, cos (x) = - \frac{3}{2}

cos (x) = - \frac{1}{4} : x = arccos (- \frac{1}{4}) + 2 πn, x = - arccos (- \frac{1}{4}) + 2 πn

cos (x) = - \frac{3}{2} :

No Solution

Combine all the solutions

x = arccos (- \frac{1}{4}) + 2 πn, x = - arccos (- \frac{1}{4}) + 2 πn

Show solutions in decimal form

x = 1.82347 \dots + 2 πn, x = - 1.82347 \dots + 2 πn

4 sin (x) cos (x) - 23 \cdot sin (x) - 2 cos (x) + 3 = 0

2 sin^{2} (θ) - 2 = 3 sin (θ)

4 sin^{2} (x) - 7 sin (x) + 3 = 0

2 sin (x - 1 0^{\circ}) = - 0.4

cot^{2} (2 x - \frac{π}{3}) = \frac{1}{3}

What is the general solution for 8cos^2(x)+14cos(x)=-3 ?
The general solution for 8cos^2(x)+14cos(x)=-3 is x=1.82347…+2pin,x=-1.82347…+2pin