equation. The second multiplicand in the expression (a x + b)x = 0 is x itself, so
x = 0
is a solution to the equation. Setting the first term equal to zero gives:
a x + b = 0
a x = −b
b
x = −
a
Now suppose the b in the quadratic equation
2
a x + bx + c = 0 , equation 1-8, is zero. In that case,
the quadratic equation reduces to:
2
a x + c = 0
which can easily be solved without the quadratic formula as follows:
a x2 = −c
2
c
x = −
a
c
x = ± −
a
where we have emphasized the fact that there are two square roots to every value by placing a
plus-or-minus sign in front of the radical.
Now, if upon arranging the given equation in the form of the quadratic equation (equation 1-8):
2
a x + bx + c = 0
you find that a, b, and c are all non-zero, then you should use the quadratic formula. Here we
present an example of a problem whose solution involves the quadratic formula:
7