document.write( "Question 160961: The completion of a certain chemical reaction is expressed by the equation y=250-5x-x^2, where y is the number of seconds needed to complete the reaction and x is the temperature in degrees Celsius at which the reaction occurs. If the reaction is complete in 200 seconds, what is the temperature at which the reaction occurs in degrees Celsius? \n" ); document.write( "

Algebra.Com's Answer #118624 by Earlsdon(6294) $\"\"$ $\"About$

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Solve for x:
\n" ); document.write( " $\"y+=+250-5x-x%5E2\"$ where y = number of seconds (200) to complete the chemical reaction and x = the temperature, in degrees celcius, at which the reaction occurs. Substitute y = 200
\n" ); document.write( " $\"200+=+250-5x-x%5E2\"$ Subtract 200 from both sides.
\n" ); document.write( " $\"0+=+50-5x-x%5E2\"$ Multiply through by -1 to ease the process a bit.
\n" ); document.write( " $\"x%5E2%2B5x-50+=+0\"$ Solve the quadratic equation by factoring.
\n" ); document.write( " $\"%28x%2B10%29%28x-5%29+=+0\"$ Apply the zero product rule: If a*b = 0, then either a = 0 or b = 0 or both.
\n" ); document.write( " $\"x%2B10+=+0\"$ or $\"x-5+=0\"$ so that...
\n" ); document.write( " $\"x+=+-10\"$ or $\"x+=+5\"$
\n" ); document.write( "So you have two answers, as you would expect from a quadratic equation, but it is reasonable to expect that chemical reactions are more likely to occur at higher temperatures than at lower temperatures, so I think that the answer would be 5 degrees celsius. \n" ); document.write( "

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