Question

Question #6c03c

Answer 1

`x = 2/3, x = -4`

Explanation:

`3x^2 + 10x = 8`

`3x^2 + 10x - 8 = 0`

`3 * (-8) = -24`

find two numbers that add to make 10 and multiply to make -24:

`12 - 2 = 10`

`12 * -2 = -24`

`3x^2 + 10x - 8 = 0`

`3x^2 + 12x - 2x - 8 = 0`

`3x (x+4) - 2(x+4) = 0`

`(3x-2)(x+4) = 0`

`3x-2 = 0` or `x+4 = 0`

`3x = 2` or `x = -4`

`x = 2/3, x = -4`

Answer 2

`x= -4, x=2/3`

Explanation:

First, let's set the quadratic equal to zero by subtracting 8 from both sides. This gives us:

`3x^2 +10x-8=0`

Now we can factor by grouping. This is a useful factoring method, as if we can break up our x term into two terms, now our factoring gets straightforward.

We can rewrite the quadratic as:
`3x^2 + color (red)(12x-2x)=0` (Notice, I did not change the properties of this equation. I only rewrote 10x as 12x-2x to aid me in factoring.)

`color(blue)(3x^2 +12x)color (purple)(-2x-8)=0`

Blue terms: Factor a 3x out to get `color (blue)(3x(x+4))`
Purple terms: Factor a -2x out to get `color (purple)(-2(x+4)`

With both the blue and purple terms, we have a `(x+4)` in common. This means we can write the factorization as `color (blue)((3x-2))color (purple)((x+4))`.

`(3x-2)(x+4)=0` is our new equation. Now, we can set both terms equal to zero to find the "zeroes".

`3x-2=0`

`=> 3x=2`

`=> color (blue)(x=2/3)`

`x+4=0`

`=> color (purple)(x= -4)`