## EQUATIONS CONTAINING VARIABLES UNDER ONE OR MORE RADICALS

Note:

• In order to solve for x, you must isolate x.

• In order to isolate x, you must remove it from under the radical.

• If there is just one radical in the equation, isolate the radical.

• Then raise both sides of the equation to a power equal to the index of the radical.

• With these types of equations, sometimes there are extraneous solutions; therefore, you must check your answers.

• If the index of the radical is even, many times there will be a restriction on the values of x.

Problem 2.3c:

Solution:

First make a note of the fact that you cannot take the square root of a negative number. Therefore, .

Add 9x to both sides of the equation so that the radical term is

isolated.

Square both sides of the equation:

Subtract 3x from and add 9 to both sides of the equation.

Solve using factoring:

and or

Check the solution x=0 by substituting 0 for x in the original equation. If after the substitution, the left side of the original equation equals the right side of the original equation, 0 is a solution.

• Left Side:

• Right Side: 3

Since the left side of the original equation equals the right side of the original equation after 0 was substituted for x, then x=0.

Check the solution by substituting -0.888889 for x in the original equation. If after the substitution, the left side of the original equation equals the right side of the original equation, -0.888889 is a solution.

• Left Side:

• Right Side: 3

Since the left side of the original equation does not equal the right side of the original equation after -0.888889 was substituted for x, then x=-0.888889 is not a solution.

You can also check the answer by graphing the equation:

The graph represents the right side of the original equation minus the left side of the original equation. There is one x-intercept, at the origin where x=0, therefore 0 is a solution to the equation.

If you would like to review the answer and solution to problem 2.3e, click on Solution.

If you would like to go back to the problem page, click on Problem.

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