Question

Which of the following are solutions to the equation below?

Check all that apply.
x²-2x-24 = 0

Answer 1

answer should be:

x=6
x=-4

Answer 2

`x=6, x=-4`

Explanation:

1) Let's solve this quadratic equation by factorizing. We need to find two numbers that multiply to -24 and add up to -2 simultaneously. If we pull out the factors of -24, two of them will be -6 and 4, which multiply to -24 as well as add up to -2.

3) Write
`-2x` as a sum.

`x^2-6x+4x-24=0`

Now, we can factor them out by grouping.

`x^2-6x+4x-24=0\\x(x-6) + 4(x-6)=0`

Since,
`x -6` is common in both of the factors, we only take one of the
`x -6` along with
`x` and
`4` and all equated to 0.

`(x-6)(x+4) = 0`

Solve for x:
`x-6=0`

`x=0+6\\x=6`

Solve for x:
`x+4=0`

`x=0-4\\x=-4`

Therefore, our solutions to this quadratic equation are
`x=6, x=-4`.