To finish our example, we need
to solve the quadratic equation
2x squared minus 4x minus 16
equals 0, which we can do using
the quadratic formula which
says that the roots of ax
squared plus bx plus c equals
0 are given by the formula
negative b plus or minus
the square root of b
squared minus 4ac all over 2a.
Wherein this example, our
coefficient of x squared,
a, is 2.
Our coefficient of
x is negative 4.
And our constant is
negative 16, giving
the formula negative
negative 4 plus or minus
the square root of negative 4
squared minus 4 times 2 times
negative 16 all over 2 times 2.
Now, we can reduce this, because
negative negative 4 is 4,
negative 4 squared is 16,
and negative 4 times 2 times
negative 16 is positive 128,
while in the denominator
we have 2 times 2, which is 4.
Now working under the
square root, 16 plus 128
is 144, whose square root is 12.
So we're left with 4
plus or minus 12/4.
4 plus 12 is 16,
which we have over 4.
And 4 minus 12 is negative 8,
which, again, we have over 4.
And these can be reduced
to 4 and negative 2.
So we can conclude that
the solutions to 2x
squared minus 4x minus 16
equals 0 are 4 and negative 2.
