## 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 2.3b:

Solution:

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

Subtract 9x from both sides of the equation so that the radical term is

isolated.

Square both sides of the equation:

Subtract 3x and 2 from both sides of the equation.

Simplify.

Check the solution by substituting 1.386897 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, 1.386897 is a solution.

• Left Side:

• Right Side: 10

Since the left side of the original equation does not equal the right side of the original equation after 1.386897 was substituted for x, then x=1.386897 is not a solution.

Check the solution x= 0.872362 by substituting 0.872362 in the original equation. If after the substitution, the left side of the original equation equals the right side of the original equation, 0.872362 is a solution.

• Left Side:

• Right Side: 10

Since the left side of the original equation equals the right side of the original equation after 0.872362 was substituted for x, then x=0.872362 is 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 only one x-intercept, at 0.872362, therefore 0.872362 is a solution to the equation.

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

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

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