Chapter 7 linear equaTionS 213

square root on one side of the equation (in this example, it already is) and
then square both sides.

x

x

x

()− =

−=

++

=

16

136

11

37

(^22)
Because we squared both sides of the equation, we need to make sure
x = 37 is a solution to the original equation.
37 − 1 = 6
is a true statement, so x = 37 is the solution.
In order for this method of square both sides of an equation to “undo” a
square root, the radical must be isolated on one side of the equation.
EXAMPLE
Solve the equation.
41 x++= 710
Before we square both sides of this equation, we must isolate the root,
41 x+ , so we subtract 7 from both sides.
41710
413
413
419
48
4
4
8
4
2
(^22)
x x x x x x x
++=
+=
()+ =
+=

=

Because we squared both sides of the equation, we must check our solution.
42 1710
9710
3710
()++=?
+=
+=
Because 3 + 7 = 10, is true, x = 2 is the solution.
EXAMPLE
Solve the equation.
EXAMPLE
Solve the equation.