Hi, welcome
to the WTAMU Virtual Math Lab.
This video
will step you through
College Algebra
Tutorial 17 Example 11.
In this example, we want to solve
the quadratic equation
x squared plus 9 equals 6x
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.
It looks like we need to bring
the 6x over to the right side.
We can do this
by subtracting both sides by 6x.
Doing this, we get
x squared plus 9 minus 6x
equals 6x minus 6x.
This will simplify to be
x squared minus 6x plus 9
equals 0.
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 these numbers.
For our problem that means
a equals 1,
b equals a negative 6,
and c equals 9.
In Step 4, we want to plug
in the values found in Step 3
into the quadratic formula,
which 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 will get x equals a negative b,
which is a negative 6,
plus or minus
the square root of b,
which is a negative 6, squared
minus 4 times a, which is 1
times c, which is 9,
all over 2 times a, which is 1.
In Step 5, we want to simplify,
if possible.
This will give us
x equals 6 plus or minus
the square root
of negative 6 squared is 36,
minus 4 times 1 times 9,
which is 36,
all over 2 times 1, which is 2.
Taking the 36 minus 36,
we get the 6 plus or minus
the square root of 0,
all  over 2,
and since
the square root of 0 is 0,
we get x equals 6/2,
which will simplify to be
x equals 3.
We cannot simplify
this any further,
so our final answer is
x equals 3.
