What is the general solution for 8cos^2(x)+14cos(x)+3=0 ?

The general solution for 8cos^2(x)+14cos(x)+3=0 is x=1.82347…+2pin,x=-1.82347…+2pin

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8cos^2(x)+14cos(x)+3=0

8 cos^{2} (x) + 14 cos (x) + 3 = 0

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

Solution steps

8 cos^{2} (x) + 14 cos (x) + 3 = 0

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

0 = 4 cos (x) sin (x) - sin (x)

sin (x) cos (x) = tan (x)

cos (x) = \frac{2}{4}

sin (x) - sin (x) \cdot cos (x) = 0

1 - 1 tan^{2} (2 x) = sec^{2} (2 x)

What is the general solution for 8cos^2(x)+14cos(x)+3=0 ?
The general solution for 8cos^2(x)+14cos(x)+3=0 is x=1.82347…+2pin,x=-1.82347…+2pin