Question

Solve each quadratic equation by factoring. Show steps pls 8x^2 - 4x = 2x +9

Answer 1

Answer:

hope these help........

Answer 2

Answer:

$x = \frac{-3}{4}$ or  $x = \frac{3}{2}$

Step-by-step explanation:

$8x^{2} - 4x = 2x +9$

Okay, let's put everything on one side.

$8x^{2} -4x-2x-9=0$

As you can see we can subtract -4x from -2x now leaving us with -6x.

$8x^{2} -6x-9=0$

Now there are multiple ways to solve a polynomial, but we can go with a way to factor them the easy way. We need to multiply the leading coefficient with the ending term because there is no common number we can factor out of these guys.

$8(-9)=-72$

We multiplied 8 and -9 together which gave us -72. With this, we need to find two numbers that add to the middle term, -6, but will multiply to -72. This is going to be 6 and -12. Now we are going to replace the middle coefficient with those two numbers.

$8x^{2} + 6x - 12x- 9= 0$

(Keep in mind the equation has not changed)

Now we are going to do something called factoring by grouping, with the first two terms, 8x^2 and 6x we take out the GCF (greatest common factor):

$2x(4x+3)$

so let's do the same between the last two.

$-3(4x+3)$

So when putting them together we have,

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

Now let's factor here, (4x+3) can be taken out and 2x as well as -3 can be put together.

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

Then we set these factors to zero to get our x answer:

$4x+3=0$

$2x-3=0$

And we solve, which leaves us with:

$x = \frac{-3}{4}$ or  $x = \frac{3}{2}$