What is the quadratic formula for (3t^(2)-10)^(2)+5(3t^(2)-10)-14=0 ? With work would be appreciated please. I'm trying to learn this, but im struggling

Question

asked Aug 13, 2021 103k views

1 Answer

Chappjc · Answer 1 · 2021-08-19T23:18:31+0000

(3t^2-10)^2+5(3t^2-10)-14=0

Suppose for the moment that you substitute
u=3t^2-10 . Then the equation becomes

u^2+5u-14=0

You could use the quadratic formula from this point, but no need, since you can easily factorize:

$u^2+5u-14=(u+7)(u-2)=0\implies u=-7\text{ or }u=2$

This in turn means

$3t^2-10=-7\text{ or }3t^2-10=2$

Can you solve for
from here?