The temperature at which the reaction occurred is T = -10⁰C or 5⁰C
Explanation:The equation representing the number of seconds to complete a chemical reaction is:
[tex]S=250-5T-T^2[/tex]If a chemical reaction was complete in 200 seconds, then S = 200
[tex]\begin{gathered} 200=250-5T-T^2 \\ \\ T^2+5T+200-250=0 \\ \\ T^2+5T-50=0 \end{gathered}[/tex]Solve for T in the quadratic equation above
[tex]\begin{gathered} T^2-5T+10T-50=0 \\ \\ T(T-5)+10(T-5)=0 \\ \\ (T+10)(T-5)=0 \\ \\ T+10=0 \\ T=-10 \\ \\ T-5=0 \\ T=5 \end{gathered}[/tex]Since T = -10 or T = 5, the temperature at which the reaction occurred is T = -10⁰C or 5⁰C
