Question

6x^2-9x+18 Please show work :)( for brainly)

Answer 1

Hey there! I'm happy to help!

This is a quadratic equation (it follows the form ax^2+bx+c). To solve these, we first want to factor. We have to find two numbers that multiply to create c and multiply to get b. We'll call these numbers s and t.

s·t=18

s+t=-9

Let's look at factors of 18.

18 and 1

2 and 9

3 and 6

We see that 3 and 6 add to make 9. But, we want -9. If we use -3 and -6, it will add to make -9 and still multiply to get 18.

So, our numbers are -3 and -6. We put this into the factored form (x+s)(x+t), so we have (x-3)(x-6). To find what x is equal to, we set that factored form equal to zero and we see what x values would give us 0.

(x-3)(x-6)=0

There are two possible ways to make this 0. The first parentheses end up equaling 0 and the second ones equal 0. If we have x-3=0, then x=3. If we have x-6=0, then we have x=6.

Therefore, the two solutions are x=3 or x=6.

Have a wonderful day! :D