Hi, welcome
to the WTAMU Virtual Math Lab.
This video
will step you through
College Algebra
Tutorial 17 Example 9.
In this example, we want to solve
the quadratic equation
2x squared minus 5x plus 1
equals 0
by using the quadratic formula.
In Step 1, we want to simplify
each side, if needed.
This equation
is already simplified.
In Step 2, we want to write
the quadratic equation
in standard form if needed.
Standard form
for a quadratic equation is
ax squared plus bx plus c
equals 0.
This equation is already
in standard form.
In Step 3, we want to identify
a, b, and c.
In standard form, a is the number
in front of x squared,
b is a number in front of x
and c is the constant.
We want to make sure
that we keep the sign
that is in front of each
of those numbers.
So for our problem,
that means a equals 2,
b equals a negative 5,
and c equals 1.
In Step 4, we want to plug
in the values found in Step 3
into the quadratic formula.
The quadratic formula is
x equals negative b plus or minus
the square root of, b squared
minus 4ac, all over 2a.
Plugging in our values
into this formula
we're going to get
x equals a negative and b is
a negative 5 plus or minus
the square root of b squared,
so we'll have
a negative 5 squared
minus 4 times a, which is 2
times c, which is 1,
all over 2 times a, which is 2.
In Step 5, we want to simplify,
if possible.
This will give us
x equals 5 plus or minus
the square root
of negative 5 squared,
which is 25,
minus 4 times 2 times 1,
which is 8,
all over 2 times 2, which is 4.
We can subtract that 25 minus 8
under the square root
and get 5 plus or minus
the square root of 17, all over 4.
This will not simplify
any further,
so our final answer is
x equals 5 plus or minus
the square root of 17, all over 4.
