>> Use the quadratic formula to solve
3x squared plus 3x minus 1 equals 0.
In this problem the value of a is 3, the value
of b is 3 and the value of c is negative 1.
And once we know the values
of those coefficients,
we can substitute them into
the quadratic formula.
Which is x equals the opposite of
b plus or minus the square root
of b squared minus 4ac all over 2a.
Let's substitute these numbers in.
We start off with the opposite
of b, in this case b is 3,
so the opposite of be is going to be negative 3.
Then plus or minus the square root of b
squared, in this case is 3 squared which is 9.
Then minus 4 times a, which is 3
times c which is negative 1 all
over 2 times a, which in this case is 2 times 3.
Now let's evaluate what's
inside that square root.
We still have negative 3 plus or minus the
square root of, now we're going to have 9
and then notice that we've got these 2
negatives that are going to cancel out.
Those are going to give us plus.
And then 4 times 3 times 1 is 12.
And then all over 2 times 3 is 6.
Now lastly under that square root we
can add 9 and 12, and 9 plus 12 is 21.
So we end up with the square
root with negative 3 plus
or minus the square root of 21 all over 6.
And we're going to split this up into
2 fractions so that we can reduce.
We've got negative 3/6 plus or
minus the square root of 21 over 6.
And the very last thing we can do is simplify
negative 3/6 is the same as negative 1/2 plus
or minus the square root of 21 over 6.
And this is what x equals and
that's as simplified as we can get.
And so our final answer is x equals negative
1/2 plus or minus the square root of 21 over 6.
