We are given the following quadratic equation
[tex]f(x)=x^2+2x-24[/tex]We can solve this equation by factoring or by using the quadratic formula.
Let us solve the equation by factoring.
We need two numbers such that their product is -24 and their sum is 2
a×b = -24
a + b = 2
How about 6 and -4?
a×b = 6×-4 = -24
a + b = 6 - 4 = 2
Now break the middle term (2x) as (6x - 4x)
[tex]\begin{gathered} x^2+2x-24 \\ (x^2+6x)-(4x-24) \end{gathered}[/tex]Take x common from the first pair and -4 from the second pair
[tex]\begin{gathered} (x^2+6x)-(4x-24) \\ x(x+6)-4(x+6) \\ (x+6)(x-4) \end{gathered}[/tex]So, the solution is
[tex]\begin{gathered} x+6=0\: \: and\: \: x-4=0 \\ x=-6\: \: and\: \: x=4 \end{gathered}[/tex]Therefore, the solution of the given quadratic equation is
[tex](-6,4)[/tex]