>> Here we are asked to solve
49 x squared plus 36 equals zero.
Notice there is no x term
appearing in this equation.
But it is, in fact, a quadratic
equation because we can write it
as 49 x squared plus zero
x plus 36 equals zero.
So, it is a quadratic
function with a equals 49.
b equals zero,
and c equals 36.
Using the quadratic formula x
would equal the opposite of b,
plus or minus the square root of
b squared minus 4ac all over 2a.
This gives us the opposite of
zero or zero, plus or minus
the square root of zero minus
4 times 49 times 36.
All over 2 times 49.
This gives us plus or minus
the square root of negative 4,
times the square root of
49, times the square root
of 36, all over 2 times 49.
Which in turn gives us plus
or minus 2i times 7
times 6, over 2 times 49.
The 2's cancel.
7 cancels.
To give us: plus or minus
six-sevenths i. Now,
the second method
is actually shorter.
In the second method, we start
with 49 X squared
plus 36 equals zero
and isolate the x squared
by first subtracting 36
and then dividing
both sides by 49.
So, x squared equals
negative 36 divided by 49.
So, x equals plus or minus
the square root of negative 36
over 49, which is plus
or minus the square root
of negative 1 times
the square root of 36,
all over the square root
of 49. Which is plus
or minus i times six-sevenths
or six-sevenths i. Both
of these methods are
quite acceptable.
