Question

решите уравнение
(|x +2|+1)x = - 4 - 4x

Answer 1

$(|x +2|+1)x = - 4 - 4x \ x+x|x+2|=-4x-4 \ x|x+2|=-5x-4 \ x(x+2)=-5x-4 ; x(x+2)=5x+4 \ x^2+2x=-5x-4= textgreater x^2+7x+4=0= textgreater x^2+7x=-4= textgreater \ = textgreater x^2+7x+49/4=33/4= textgreater (x+7/2)^2=44/3= textgreater x+7/2= \ = frac{ sqrt{33} }{2}= textgreater x= frac{ sqrt{33} }{2} -7/2 \ x+7/2=- frac{ sqrt{33} }{2} = textgreater x=-7/2- frac{ sqrt{33} }{2} \ x^2+2x=5x+4= textgreater x^2-3x-4=0= textgreater (x-4)(x+1)=0 \ x-4=0= textgreater x=4 \ x+1=0= textgreater x=-1$

Ответ: $x= frac{ sqrt{33} }{2} - frac{7}{2}$