help what is x^2-2x-24=0 I know you can use quadratic formula I just forgot how examples always help :)

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[latex]x^2-2x-24=0\\\\a=1;\ b=-2;\ c=-24\\\\\Delta=b^2-4ac\\\\\Delta=(-2)^2-4\cdot1\cdot(-24)=4+96=100\\\\x_1=\frac{-b-\sqrt\Delta}{2a};\ x_2=\frac{-b+\sqrt\Delta}{2a}\\\\x_1=\frac{2-\sqrt{100}}{2\cdot1}=\frac{2-10}{2}=\frac{-8}{2}=-4\\\\x_2=\frac{2+\sqrt{100}}{2\cdot1}=\frac{2+10}{2}=\frac{12}{2}=6[/latex]


There are another way to solve a quadratic equation we call, Sum and product. Let's see how we can do this... [latex]x^2-2x-24=0[/latex] [latex]Sum=-\frac{b}{a}[/latex] [latex]Product=\frac{c}{a}[/latex] therefore [latex]Sum=-\frac{(-2)}{1}=2[/latex] [latex]Product=\frac{-24}{1}=-24[/latex] now we have to pick up 2 numbers that the sum should be 2 and the product should be -24, we just have to think a little. Let's try -3 and 8, for example. [latex]8+(-3)=5[/latex] [latex]8*(-3)=-24[/latex] Doesn't work. Let's try now 4 and -6. [latex]4+(-6)=-2[/latex] [latex]4*(-6)=-24[/latex] Can you see here, that we have to change the signal?! therefore Let's try -4 and 6 [latex]6+(-4)=2[/latex] [latex]6*(-4)=-24[/latex] [latex]Sum=2[/latex] and [latex]Product=-24[/latex] Them it works. [latex]\boxed{\boxed{x_1=-4~~and~~x_2=6}}[/latex]

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