Question

Please help me, I am, tired.

Show all work to solve 3x^2 − 5x − 2 = 0.
If you answer, please tell me the reason for your steps. I've fallen behind in Algebra and need visuals to finally understand.

Answer 1

(2,0) and (-1/3,0)

x = 2

x = -1/3

Explanation:

Hi there!

You'll notice that this equation is a quadratic. When graphed, this equation looks like a parabola that crosses the x-axis at two points, which can be written as ordered pairs with an x value and a y value.

We know that both of these points will have a y value of 0, but we don't know what the x values of the points are—these are what we want to find.

(Check out the graphing program Desmos—type in your equation and it will graph it out for you.)

Notice that your equation follows this structure:

`ax^2+bx+c=0`

In our case,

`a=3\\b=-5\\c=-2`

We can plug our values of a, b, and c into the quadratic equation to find the two x values.

I've attached a picture of my work. At the top is the quadratic equation. I substituted our values in and solved.

You'll notice that the answer I ended up with has a ± symbol. We have to simplify this down two different ways to get our two answers: once using the plus sign, once using the minus sign. This will give us two different values for x.

We'll start with the plus sign:

`(5+7)/(6) \\=2`

So: one of our x values is 2.

Now the minus:

`(5-7)/(6) \\=-(1)/(3)`

Our other x value is -1/3.

You can check to make sure these answers work by plugging them back into the original equation for x. If they work, the left side of the equation should boil down to 0.

Let me know if you have any other questions! Best of luck with getting caught up in Algebra!