polynomial problem

The left side of a solid block is held at a constant temperature of 200 degrees Celsius. The temperature profile within the block is given by T=200-5x-x^2 where x is the distance from the left side of the block in centimeters and T is the temperature in degrees Celsius of the block at location x. At what value of x is T=50 degrees celsius.

I have not had algebra in many years, and have forgotten how to solve this. I tried to solve for x and substitute back into the original equation, but i keep doing something wrong. I know I need two equations, but am struggling on how to do this. Please help.

Since T = 200 - 5x - x^2 and T = 50, then:
200 - 5x - x^2 = 50
x^2 + 5x - 150 = 0
(x + 15)(x - 10) = 0

I'll leave you with the fun of finishing it :wink:

thank you dennis. your reply at least confirms the work i've done to this point, but it is at this point that i'm struggling on how to finish the problem. i'm confused as how to solve for x.

If you had shown your work - as specified in the "read before posting thread - then neither Denis nor you would be wasting time redoing what you have presumably already done (nor me writing this). You would have gotten hint for the next step as follows:

If

\(\displaystyle A \times B \, = \, 0\)

then

either

\(\displaystyle A \, = 0\)

or/and

\(\displaystyle B \, = 0\)

Please show your work indicating exactly where you are stuck, so that we know where to begin to help you.

I apologize for not showing my work. my mistake - won't happen again. Appreciate your help with this problem. Now, I understand it. Thanks again.