Due to the properties of the square root function,
[tex]\begin{gathered} \sqrt[]{(x+1)}\to\text{exists} \\ \Rightarrow x+1\ge0 \\ \Rightarrow x\ge-1 \\ \text{and} \\ \sqrt[]{y}\ge0 \end{gathered}[/tex]Solving the equation,
[tex]\begin{gathered} 4+\sqrt[]{(x+1)}=0 \\ \Rightarrow\sqrt[]{(x+1)}=-4!!! \end{gathered}[/tex]This is not possible since the square root is always greater or equal to zero; therefore, the equation has no solutions.
There is no real number such that multiplied by itself is equal to -4
