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Which of the following are solutions to the equation below?
Check all that apply.
x²-2x-24 = 0

Sagot :

johnny837

Answer:

[tex]x=6, x=-4[/tex]

Step-by-step 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 [tex]-2x[/tex] as a sum.

[tex]x^2-6x+4x-24=0[/tex]

Now, we can factor them out by grouping.

[tex]x^2-6x+4x-24=0\\x(x-6) + 4(x-6)=0[/tex]

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

[tex](x-6)(x+4) = 0[/tex]

Solve for x: [tex]x-6=0[/tex]

[tex]x=0+6\\x=6[/tex]

Solve for x: [tex]x+4=0[/tex]

[tex]x=0-4\\x=-4[/tex]

Therefore, our solutions to this quadratic equation are  [tex]x=6, x=-4[/tex].
answer should be:

x=6
x=-4
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