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