Verified answer

*x = 3*

Check the answer by plugging in 3 into the equation

You get 63 - 39 - 24 = 0

You could use the quadratic formula, or you could factor it.

Let's factor it...

7x^2 - 13x - 24 = 0

The way to factor this is to multiply the first and last terms:

(7x^2)(-24) = -168x^2.

Now, find two factors of -168x^2 that add to make the middle term, which is -13x. After a few trials, we see that -21x and 8x multiply to make -168x^2 and add to make -13x, so, we use those two terms (-21x and 8x) to rewrite the middle term.

--> 7x^2 - 21x + 8x - 24 = 0

Factor the first two and second two terms separately...

--> 7x(x - 3) + 8(x - 3) = 0

Factor out the common (x - 3)...

--> (7x + 8)(x - 3) = 0

Now, by the zero product rule, you can set each factor equal to zero and solve...

7x + 8 = 0

--> x = -8/7

x - 3 = 0

--> x = 3

There are two solutions: x = -8/7 and x = 3.

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If I use the quadratic formula to solve this, I will get the same answer as shown below. (Remember that the quadratic formula can be used when a quadratic equation is such that the right side of the equation is zero...as in this case.)

7x^2 - 13x - 24 = 0

--> a = 7, b = -13, and c = -24

Quadratic Formula:

x = [-b +- sqrt(b^2 - 4ac)] / (2a)

--> x = [-(-13) +- sqrt((-13)^2 - 4(7)(-24))] / (2*7)

--> x = [13 +- sqrt(169 + 672)] / (2*7)

--> x = (13 +- sqrt(841)) / 14

--> x = (13 +- 29) / 14

So, using the quadratic formula, we get two solutions again...

x = (13-29)/14 = -16/14 = -8/7

and

x = (13+29)/14 = 42/14 = 3

We get the same two solutions: x = -8/7 and x = 3.

Well, the answers are going to be {-8/7, 3}

Here is how you get them:

You first will see if you can take out a GCF. You can't because nothing goes into 7, 13, and 24 at the same time.

Now, you are going to factor it. After factoring it, you are going to have:

7x^2-21x+8x-24=0 (If you don't know how to do that, tell me.)

Then you are going to do this by grouping. After grouping, you are going to have:

7x(x-3)+8(x-3)=0 (If you don't know how to do that, tell me.)

Then you are going to combine it, and you will get:

(x-3)(7x+8)=0

Then you are going to set each to 0 and you are going to get:

x-3=0

and

7x+8=0

Solving both you will get:

{-8/7, 3}

If this is confusing, e-mail me.

Hope this helps :)

(7x+8)(x-3)