To finish this example, we
need to find the solutions
to the equation
negative 2x squared
plus 4x plus 6 equals 0.
Remember, the quadratic formula
says that the roots r1 and r2
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,
where our a, b, and c are given
as the coefficients of x
squared, x, and the constant.
In this case, our a, the
coefficient of x squared,
is negative 2.
The b, the coefficient
of x, is 4.
And our constant c is 6.
Putting these into
our formula, we
get that the roots are
negative 4 plus or minus
the square root of 4 squared
minus 4 times negative 2 times
6 all over 2 times negative 2.
This we can simplify
because 4 squared is 16,
negative 4 times negative 2
is 8, times 6 is positive 48,
and 2 times negative
2 is negative 4.
Under the square
root, 16 plus 48
is 64, whose square root is 8.
So we're left with
negative 4 plus
or minus 8 over negative 4.
Negative 4 plus 8 is
4 over negative 4,
and negative 4 minus 8 is
negative 12 over negative 4,
which can be reduced
to negative 1 and 3.
So we found that the
solutions to negative 2x
squared plus 4x plus 6 equals 0
are x equals negative 1 and 3.
