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.

*Example*: Solve for *x*: (*x* + 5)^{2} = 18.

= .

|x+ 5| = 3.x+ 5 = 3 orx+ 5 = - 3.x= 3 - 5 orx= - 3 - 5.

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 = - 2*x*:

()^{2} = (- 2*x*)^{2}.

6*x* + 10 = 4*x*^{2}.

4*x*^{2} - 6*x* - 10 = 0.

2(2*x*^{2} - 3*x* - 5) = 0.

2(*x* + 1)(2*x* - 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 = - 2*x* is *x* = - 1.

As demonstrated by this example, we must check *all* "solutions" and
eliminate false solutions.

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