To finish our problem,
we need to solve
the quadratic equation x squared
plus 4x minus 21 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 negative b
plus or minus the square root
of b squared minus 4ac all over
2a, where, in this example,
a is our coefficient of
x squared, which is 1,
b is our coefficient
of x, which is 4,
and c is our constant
coefficient negative 21.
Putting these into
our formula, we
have that our roots are
negative 4 plus or minus
the square root of 4 squared
minus 4 times 1 times negative
21 all over 2 times 1.
But we can simplify this
because 4 squared is 16,
negative 4 times 1 times
negative 21 is positive 84,
and 2 times 1 is 2.
So this becomes negative 4 plus
or minus the square root of 16
plus 84 all over 2.
And 16 plus 84 is 100,
so we have negative 4
plus or minus the square
root of 100 over 2,
which is negative 4
plus or minus 10 over 2.
Simplifying each
of these cases, we
get negative 4 plus 10 is
6/2, and negative 4 minus 10
is negative 14, which is over 2.
And this reduces to
3 and negative 7.
So we get that
the solutions to x
squared plus 4x
minus 21 equals 0
are x equals 3 and negative 7.
