In this section, you will solve equations with a square root containing a variable and there will be a variable on the opposite side.

Example:  Solve the equation  x = √3x + 10

Step 1: Isolate the square root on one side of the equation.  The square root is already on one side of the equation.

x =
√3x + 10
Step 2:  Square BOTH sides of the equation. 
(x)2 =
(√3x + 10)2

Step 3:  Simplify and Solve. 

x2 =

3x + 10

Steps for solving x^2-3x-10=0

Step 4:  Check your answer to see if it makes the original equation true.

Checking the answers shows that x=-2 is an extraneous root; x=5 is a solution to the equation.

What is an extraneous root?

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Solve the equation x = √6x  − 5. Click on the blanks to reveal the answer.

Interactive button. Assistance may be required. _________ x 2 = Interactive button. Assistance may be required. _________ 6x − 5

Interactive button. Assistance may be required. _________ x2 − 6x + 5 = 0

( Interactive button. Assistance may be required. _________ (x − 5) ) ( Interactive button. Assistance may be required. _________ (x − 1) ) = 0

x = Interactive button. Assistance may be required. _________ 5 or x = Interactive button. Assistance may be required. _________ 1

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