Question 160961
Solve for x:
{{{y = 250-5x-x^2}}} 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
{{{200 = 250-5x-x^2}}} Subtract 200 from both sides.
{{{0 = 50-5x-x^2}}} Multiply through by -1 to ease the process a bit.
{{{x^2+5x-50 = 0}}} Solve the quadratic equation by factoring.
{{{(x+10)(x-5) = 0}}} Apply the zero product rule: If a*b = 0, then either a = 0 or b = 0 or both.
{{{x+10 = 0}}} or {{{x-5 =0}}} so that...
{{{x = -10}}} or {{{x = 5}}}
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.