Now it's your turn to solve a quadratic equation
using the quadratic formula. Stop this video,
take a moment to write out your answer to
this problem in your lecture outline packet,
and then turn the video back on to check your
answer. The equation that we're asked to solve
is x² + 2 = -7x. And on the page here,
I've written down the quadratic formula, which
states that if ax² + bx + c = 0, then
x equals the opposite of b plus or minus the
square root of the quantity b² - 4ac all
over 2a. So let's get started with this problem,
x² + 2 = -7x. So our original equation….
And in order to use the quadratic formula,
we'll need to set this equation equal to 0.
We'll do that by adding 7x to each side of
the equation. And that will give us x² +
7x + 2 = 0. Now we're ready to apply
the quadratic formula. So from here, we can
then state that x equals the opposite of b,
which will be -7 plus or minus the square
root. And we need b², which is 7² minus--.
And now we need 4ac, which will be 4(1)(2).
And that's all divided by 2(a), which in this
case is 2(1). So from here, we'll simplify
what's inside the radical. And then we'll
simplify the fraction, if possible. So writing
this solution, or these solutions-- there
are we going to be two of them, we have x
equal to -7 plus or minus--. And then inside
that radical, we have 7² - 4(1)(2). So that
will be 49 - 8. And again, that's all divided
by 2. Continuing, we can state then that x
is equal to -7 plus or minus the square root
of 41, which we calculated by taking 49 - 8.
And that's still all divided by 2. The square
root of 41 cannot be simplified because it
does not have any perfect square factors.
So at this point, the solutions that we have
are fully simplified. To check these solutions,
we would replace every instance of x in the
original equation with -7 plus the square
root 41 all over 2. And -7 minus the square
root 41 all over 2. We check each of those
solutions. We could also take decimal approximations
and check them. We're going to omit the checks
here and simply state the solution set. So
the solution set here, I'm going to write
curly brackets to show that this is the set
of all solutions. And then we'll have one
solution, which is -7 plus the square root
of 41. And that expression is divided by 2.
Then we'll separate it with a comma, and put
-7 minus the square root of 41. And that expression
is divided by 2. And then, of course, these
two numbers are in curly brackets.
