Solving an Equation with Two Radical Terms
Example
Solve for x:
Solution Step 1 Isolate a radical term.
Subtract
from both sides.
Step 2 Apply the Principle of Powers.


= 2

Square both sides. 


Step 3 Solve the resulting equation.
Write the right side as a product. 

FOIL the right side.


Isolate the remaining radical term.

2x  6 

Divide both sides by 2.

x  3 

Square both sides.

(x  3)^{2} 

Write the left side as a product.
Simplify.
Write in standard form.
Factor.
Use the Zero Product Property.
Solve for x. Step 4 Check the solution. 
(x  3)(x  3)
x^{2}  6x + 9
x^{2}  10x  21
(x  3)(x  7)
x  3 = 0 or x  7
x = 3 or x 
= 4(x  3)
= 4x  12
= 0
= 0
= 0
= 7 
Since x = 7 does not check, the only solution is x
= 3.
Note:
We divide both sides by 2 rather than 4 in
order to avoid introducing fractions into
the equation.
One way to simplify
is:
