For what value of c is the expression x2 + 10x + c + 2 a perfect square?

A quadratic expression in the form $x^2 + Bx + C$ is a perfect square if it can be written as $(x+k)^2$.
Expanding $(x+k)^2$ gives $x^2 + 2kx + k^2$.

The given expression is $x^2 + 10x + c + 2$.
Comparing coefficients with $x^2 + 2kx + k^2$:
The coefficient of $x$ is 10, so $2k = 10$.
The constant term is $c+2$, so $k^2 = c+2$.

From $2k = 10$, we find $k$:

Substitute the value of $k$ into the equation for the constant term:

Subtract 2 from both sides to find $c$:

The value of $c$ is $\boxed{23}$.