What is the general solution for cos^2(x)-7cos(x)-1=0 ?

The general solution for cos^2(x)-7cos(x)-1=0 is x=1.71131…+2pin,x=-1.71131…+2pin

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cos^2(x)-7cos(x)-1=0

cos^{2} (x) - 7 cos (x) - 1 = 0

x = 1.71131 \dots + 2 πn, x = - 1.71131 \dots + 2 πn

Solution steps

cos^{2} (x) - 7 cos (x) - 1 = 0

Solve by substitution

cos (x) = \frac{7 + 53}{2}, cos (x) = \frac{7 - 53}{2}

cos (x) = \frac{7 + 53}{2} :

No Solution

cos (x) = \frac{7 - 53}{2} : x = arccos (\frac{7 - 53}{2}) + 2 πn, x = - arccos (\frac{7 - 53}{2}) + 2 πn

Combine all the solutions

x = arccos (\frac{7 - 53}{2}) + 2 πn, x = - arccos (\frac{7 - 53}{2}) + 2 πn

Show solutions in decimal form

x = 1.71131 \dots + 2 πn, x = - 1.71131 \dots + 2 πn

sec^{2} (x) + tan (x) - 1 = 0

0 = sin (θ)

6 tan^{4} (x) - tan^{2} (x) - 2 = 0

t, x = sin (t)

2 sin^{2} (x) - 2 = 0

What is the general solution for cos^2(x)-7cos(x)-1=0 ?
The general solution for cos^2(x)-7cos(x)-1=0 is x=1.71131…+2pin,x=-1.71131…+2pin