Question

Question was provided via image upload.

Explanation:

Step1: Analyze left-hand side property

The square of any real number $(x+1)^2 \geq 0$ for all real $x$.

Step2: Compare with right-hand side

The right-hand side is $-40 < 0$, so no real $x$ satisfies the equation. Also, $\sqrt{-40}$ is not a real number (it is imaginary).

Answer:

The equation $(x + 1)^2 = -40$ has $\boldsymbol{0}$ real solution(s) because $\sqrt{-40}$ is $\boldsymbol{\text{an imaginary number}}$.