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(male narrator) In this video,
we will look at using the quadratic formula
when one or more of the terms is missing.
If a term is missing, we will simply use 0
as we plug in values for the quadratic formula.
For example, in this problem,
you may notice that there is no x term.
This means we can think
about there being 0x in the middle.
So 7 would be our a;
and for b, we'll use that 0; while -49 is our c.
Plugging these values into the quadratic formula,
we have x equals the opposite of b, or 0;
plus or minus the square root of b, or 0 squared;
minus 4a, which is 7;
c, which is -49; all over 2a, which is 7.
We can ignore the 0s,
as they won't have any effect on our problem,
and we get x is equal
to plus or minus the square root of 4 times 7;
times 49, is 1,372; over 2 times 7, which is 14.
To simplify that radical,
we'll need to find out what goes into 1,372;
which is divisible by 2, 686 times;
which is divisible by 2, 343 times;
which is divisible by 7, 49 times;
which is divisible by 7, 7 times; and 7, once.
So now, we have x is equal
to plus or minus the square root of 2 squared,
times 7 cubed, over 14.
We can take the square root of 2 squared,
dividing the exponent by the index,
and the 7 cubed, with one 7 remaining behind.
We now have x is equal to plus or minus;
2 times 7 is 14;
square root of 7; over 14;
14s divide out; and for our final answer,
x is equal to plus or minus the square root of 7.
Let's try one more problem
where we have to use 0 for a missing term
and simplify what remains in the quadratic formula.
Again, you notice the x term is missing,
so we'll think about this as having 0x:
a is 3, b is 0, and c is 54.
Plugging these values in the quadratic formula,
we get x is equal to the opposite of b, or 0;
plus or minus the square root of b, or 0 squared;
minus 4a, which is 3; times c, which is 54;
all over 2a, which is 3.
The 0s can be ignored as we multiply what's left together:
x is equal to plus or minus the square root of -4 times 3;
times 54, is -648; all over 2 times 3, which is 6.
We can then factor what's left
to see if we can simplify that radical.
If it's negative, we'll use -1 as a factor
and then see how 648 can be factored out.
It's divisible by 4...or 2, sorry...2, 324 times;
which is divisible by 2, 162 times;
which is divisible by 2, 81 times;
which is divisible by 3, 27 times;
3, 9 times; 3, 3 times; and 3, once.
This means we have factors:
2 cubed, times 3 to the 4th, all over 6.
We can pull a 2 cubed out with one 2 remaining;
3 to the 4th will come out as 3 squared, or 9;
and then -1 will come out as an i.
This means we have x is equal to plus or minus 18i,
times the square root of 2, over 6.
We can then simplify the 18 over 6 to get 3,
and x is equal to plus or minus 3i,
times the square root of 2,
and this becomes our final solution.
As you can see, if a term is missing,
we simply use 0 for that term
and can use the quadratic formula like always--
simplifying the entire expression.