In this video, we will be
solving a quadratic equation using the quadratic formula.
Here, we have the equation
2x squared minus 3x minus 4 equal 0,
and we would like to find its solutions.
Before we get started, remember, the quadratic formula is:
x equals -b plus/minus the square root of
b squared minus 4ac
all over 2a.
Since the given equation is already in the form
of ax squared plus bx plus c equals zero,
we don't have to do any rearranging.
But if it wasn't, then before using the formula,
we would have to rearrange the equation into
"ax squared plus bx plus c equals zero" form.
Now, for this quadratic equation,
our a-value is 2,
our b-value is -3,
and our c-value is -4.
Next, we just need to substitute
these three values into the quadratic formula like so.
This gives us x equals
negative, bracket -3, plus/minus
square root of -3 all squared,
minus 4 times 2 times -4
all over 2 times 2.
Then, to compute our solutions,
we just have to multiply out all the
values in our formula
and get rid of all the brackets,
and simplify our answer.
In this middle step, we have 3 plus/minus square root of 9 plus 32 all over 4
Then, we can simplify
that into 3 plus/minus square root of 41
over 4.
So the two exact solutions
we got from the formula are:
x equals 3 plus square root of 41 all over 4,
and x equals 3 minus square root of 41 over 4.
You might be asked to find
the rounded solutions,
so using our calculator, rounding to two decimal places,
we have 2.35 and -0.85,
giving us the two solutions to
our giving quadratic equation:
2x squared minus 3x minus 4 equals zero.
