### Video Transcript

Solve seven 𝑥 squared plus twelve
𝑥 plus two equals zero. So this time, 𝑎 is seven, 𝑏 is
twelve, and 𝑐 is two. They’re all positive. So I can put those into the
formula. And then I get negative twelve plus
or minus the square root of twelve squared minus four times seven times two all over
two times seven, just by plugging in 𝑎, 𝑏 and 𝑐 into that formula. Well twelve squared is a hundred
and forty-four, and four times seven is twenty-eight, and twenty-eight times two is
fifty-six, so we’re subtracting fifty-six from that.

And again, we’ve got two
values. Either 𝑥 is equal to negative
twelve plus root eighty-eight all over fourteen or 𝑥 is equal to negative twelve
minus root eighty-eight all over fourteen. Now root eighty-eight turns out to
be an irrational number. We can’t just find a nice easy
integer square root for it. So typically, in these questions
you would either give your answer in its simplest surd form, or you would round to a
specific number of decimal places. So either 𝑥 is equal to negative
six plus root twenty-two over seven, which is minus nought point one nine to two
decimal places, or 𝑥 is equal to negative six take away root twenty-two all over
seven which is equal to minus one point five three to two decimal places. So that was probably a more typical
example of the sort of question you’d be asked to answer, where the original
expression up here didn’t factor nicely, so we couldn’t come up with nice simple
answers.