What Are the Values of c for Continuity at x=5?

[togame]

Homework Statement

$$f(x) = x^2 - c^2 \mbox{ if } x < 5$$
$$f(x) = cx+11 \mbox{ if } x \geq 5$$

Find the two values of c for which the function would be continuous.

Homework Equations

The Attempt at a Solution

I set these two equations equal to each other, plug in the value 5 since that is the point at which these equations would meet, then solve for c? I'm not sure if I'm missing a step in the algebra or something else, but I seem to be unable to get the correct answer.

 

[SammyS]

Homework Statement

$$f(x) = x^2 - c^2 \mbox{ if } x < 5$$
$$f(x) = cx+11 \mbox{ if } x \geq 5$$

Find the two values of c for which the function would be continuous.

Homework Equations

The Attempt at a Solution

I set these two equations equal to each other, plug in the value 5 since that is the point at which these equations would meet, then solve for c? I'm not sure if I'm missing a step in the algebra or something else, but I seem to be unable to get the correct answer.

Technically: You should find the limit of f(x) as x approaches 5 from the left, and then from the right and set the limits equal to each other, solving for c. Also, make sure that f(5) is the same as those limits.

Of course, when you do that, you do get $(5)^2-c^2=5c-11\,.$