Question

Solve for x
6x²+2x-12​

Answer 1

Explanation:

Solving for x means you have to factor. First factor out the GCF of 2 to get:

`2(3x^2+x-6)` and now we'll factor using the regular old method of ac and then factoring by grouping. In our polynomial, a = 3, b = 1, c = -6. Therefore, a times c is 3 * -6 which is -18. We need some combinations of the factors of 18 that will add to give us 1, the b term in the middle. The factors of 18 are:

1, 18

2, 9

3, 6 and that's it. Hm...it seems that won't work, so let's throw this into the quadratic formula, going back to the original and a = 6, b = 2 and c = -12:

`x=(-2+/-√(2^2-4(6)(-12)) )/(2(6))` and

`x=(-2+/-√(4+288) )/(12)` and

`x=(-2+/-√(292) )/(12)` and

`x=(-2+/-√(4*73) )/(12)` and

`x=(-2+/-2√(73) )/(12)` which finally simplifies to

`x=(-1+/-√(73) )/(6)` No wonder that didn't factor using the traditional method of factoring! We could have found that out by finding first the value of the discriminant, but oh well!