Answer:
The solution to the quadratic equation is;
[tex]\begin{gathered} n=9 \\ or \\ n=-5 \end{gathered}[/tex]
Explanation:
Given the equation;
[tex]100+(n-2)^2=149[/tex]
Let us convert the equation to a quadratic equation and solve;
[tex]\begin{gathered} 100+(n-2)^2=149 \\ (n-2)^2=149-100 \\ (n-2)^2=49 \\ \text{expanding;} \\ n^2-4n+4=49 \\ n^2-4n+4-49=0 \\ n^2-4n-45=0 \end{gathered}[/tex]
Let us solve the quadratic equation for n;
[tex]\begin{gathered} n^2-4n-45=0 \\ \text{factoring} \\ n^2-9n+5n-45=0 \\ n(n-9)+5(n-9)=0 \\ (n-9)(n+5)=0 \\ \therefore \\ n-9=0 \\ n=9 \\ or \\ n+5=0 \\ n=-5 \end{gathered}[/tex]
Therefore, the solution to the quadratic equation is;
[tex]\begin{gathered} n=9 \\ or \\ n=-5 \end{gathered}[/tex]
