MHB Is It Possible to Solve This Corrected Quartic Polynomial Equation?

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\[x^4+16x-12=0\]

\[x^{4}-12+16+16x-16=0\]

\[x^{4}+4x^{2}+4-4x^{2}+16x-16=0\]

\[(x^{2}+2)^{2}-(2x-4)^{2}=0\]

\[(x^{2}-2x+10)(x^{2}+2x-2)=0\]
 
Nice solution! There is a typo for the first factor: it should be $x^2-2x+6$
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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