To solve a radical equation, perform inverse operations in the usual way. But
take note:
= | a|, and thus expressions such as
must be solved as absolute value expressions for more on solving
equations containing absolute values. It is not necessary to solve
(
)2 as an absolute value expression.
Since we cannot take the square root of a negative number, there
are often numbers which appear to be solutions but do not actually make the
equation true. For example, we get two solutions when we solve
= - 2x:
()2 = (- 2x)2.
6x + 10 = 4x2.
4x2 - 6x - 10 = 0.
2(2x2 - 3x - 5) = 0.
2(x + 1)(2x - 5) = 0.
x = - 1 or
.
We can plug -1 in for
x in the original equation to check that it makes the
equation true:
= - 2(- 1)?
= 2? Yes.
True.
However, when we plug
in for
x:
= - 2()?
= - 5? No.
False.
is an extraneous solution, and the only solution to
= - 2x is
x = - 1.
= 
