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x^2+2y^2+2xy+4yz+5z^2=0 canonical form

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 2      2      2                    
x  + 2*y  + 5*z  + 2*x*y + 4*y*z = 0
$$x^{2} + 2 x y + 2 y^{2} + 4 y z + 5 z^{2} = 0$$
x^2 + 2*x*y + 2*y^2 + 4*y*z + 5*z^2 = 0