crystal436
1

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

$x^2-2x-24=0\\\\a=1;\ b=-2;\ c=-24\\\\\Delta=b^2-4ac\\\\\Delta=(-2)^2-4\cdot1\cdot(-24)=4+96=100\\\\x_1=\frac{-b-\sqrt\Delta}{2a};\ x_2=\frac{-b+\sqrt\Delta}{2a}\\\\x_1=\frac{2-\sqrt{100}}{2\cdot1}=\frac{2-10}{2}=\frac{-8}{2}=-4\\\\x_2=\frac{2+\sqrt{100}}{2\cdot1}=\frac{2+10}{2}=\frac{12}{2}=6$
There are another way to solve a quadratic equation we call, Sum and product. Let's see how we can do this... $x^2-2x-24=0$ $Sum=-\frac{b}{a}$ $Product=\frac{c}{a}$ therefore $Sum=-\frac{(-2)}{1}=2$ $Product=\frac{-24}{1}=-24$ 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. $8+(-3)=5$ $8*(-3)=-24$ Doesn't work. Let's try now 4 and -6. $4+(-6)=-2$ $4*(-6)=-24$ Can you see here, that we have to change the signal?! therefore Let's try -4 and 6 $6+(-4)=2$ $6*(-4)=-24$ $Sum=2$ and $Product=-24$ Them it works. $\boxed{\boxed{x_1=-4~~and~~x_2=6}}$