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

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Question 174881: 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(28504) About Me  (Show Source):
You can put this solution on YOUR website!
t+=+200+-+5x+-+x%5E2 Start with the given equation.


t+=++-+x%5E2-+5x%2B200+ Rearrange the terms.


50+=++-+x%5E2-+5x%2B200+ Plug in t=50


0+=++-+x%5E2-+5x%2B200-50+ Subtract 50 from both sides.


0+=++-+x%5E2-+5x%2B150+ Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=-1, b=-5, and c=150


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%28-1%29%28150%29+%29%29%2F%282%28-1%29%29 Plug in a=-1, b=-5, and c=150


x+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%28-1%29%28150%29+%29%29%2F%282%28-1%29%29 Negate -5 to get 5.


x+=+%285+%2B-+sqrt%28+25-4%28-1%29%28150%29+%29%29%2F%282%28-1%29%29 Square -5 to get 25.


x+=+%285+%2B-+sqrt%28+25--600+%29%29%2F%282%28-1%29%29 Multiply 4%28-1%29%28150%29 to get -600


x+=+%285+%2B-+sqrt%28+25%2B600+%29%29%2F%282%28-1%29%29 Rewrite sqrt%2825--600%29 as sqrt%2825%2B600%29


x+=+%285+%2B-+sqrt%28+625+%29%29%2F%282%28-1%29%29 Add 25 to 600 to get 625


x+=+%285+%2B-+sqrt%28+625+%29%29%2F%28-2%29 Multiply 2 and -1 to get -2.


x+=+%285+%2B-+25%29%2F%28-2%29 Take the square root of 625 to get 25.


x+=+%285+%2B+25%29%2F%28-2%29 or x+=+%285+-+25%29%2F%28-2%29 Break up the expression.


x+=+%2830%29%2F%28-2%29 or x+=++%28-20%29%2F%28-2%29 Combine like terms.


x+=+-15 or x+=+10 Simplify.


So the possible answers are x+=+-15 or x+=+10

Since "x" is the position, this means that a negative position doesn't make sense. So the value x+=+-15 can be ignored.


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Answer:

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