In this section, there will be square roots containing variables on both sides of the equation.

Example:  Solve the equation  √8x − 1 = √5x + 20

Step 1: Isolate the square root on one side of the equation.
There are square roots on both sides of the equation, they are both isolated.
√8x − 1 = √5x + 20
Step 2:  Square BOTH sides of the equation.   
(√8x − 1)2 = (√5x + 20)2
Step 3:  Simplify and Solve.        
8x − 1 = 5x + 20
 
3x = 21
 
x = 7
Step 4:  Check your answer to see if it makes the original equation true. √8x − 1 = √5x + 20 → √8(7) − 1 = √5(7) + 20 → True!

So, the final answer is  x = 7  

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Solve the equation √1 − 4x = √x + 11. Click on the blanks to reveal the answer.

√1 − 4x = √x + 11

Interactive button. Assistance may be required. _________ 1 − 4x = Interactive button. Assistance may be required. _________ x + 11

Interactive button. Assistance may be required. _________ -5x = 10

x = Interactive button. Assistance may be required. _________ -2

Be sure to check to make sure that your answers make the equation true.

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