SOLUTION: I have a block with one edge at a known temp. of 200 degrees C. The temp varies through the block according to the equation: t = 200 - 5x

SOLUTION: I have a block with one edge at a known temp. of 200 degrees C. The temp varies through the block according to the equation: t = 200 - 5x - x^2 What is x when t = 50? t=t

Question 174882: I have a block with one edge at a known temp. of 200 degrees C. The temp varies through the block according to the equation:
t = 200 - 5x - x^2
What is x when t = 50?
t=temp.
x=position
I've tried solving for x and substituting into the original equation, but it's been a long time since i had algebra, and i'm doing something wrong. this appears to be a very problem, and i'm feeling might stupid right now. any help is greatly appreciated.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Rearrange the terms.

Plug in

Subtract 50 from both sides.

Combine like terms.

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the possible answers are or

Since "x" is the position, this means that a negative position doesn't make sense. So the value can be ignored.

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Answer:

So the solution is which means that at 10 units (or whatever units you're dealing with), the temperature will be 50 degrees.
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