To finish our problem,
we need to solve
the quadratic equation x squared
minus 7x plus 10 equals 0.
We can do this using the
quadratic formula, which
says that our 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.
And in this example our a is 1--
the coefficient of x squared--
b is negative 7-- our
coefficient of x-- and c
is 10-- our constant
coefficient.
So putting this into
our quadratic formula,
we have negative
negative 7 plus or minus
the square root of negative 7
squared minus 4 times 1 times
10 all over 2 times 1.
Now negative
negative 7 is just 7.
Negative 7 squared is
49, while 4 times 1 times
10 is 40 all over 2
times 1, which is 2.
So we have 7 plus or
minus the square root
of 49 minus 40 all over 2,
but 49 minus 40 is just 9.
So we have 7 plus or
minus the square root of 9
all over 2, where the
square root of 9 is 3.
And 7 plus or minus 3 over 2
is 7 plus 3, which is 10 over 2
and 7 minus 3,
which is 4 over 2.
And these two solutions can
be reduced because 10 over 2
is 5, while 4 over 2 is just 2.
So we find that the solutions
to x minus 7x plus 10 equals 0
are 5 and 2.
