## 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.

Example 2:

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

Subtract 5x from both sides of the equation so that the radical term is isolated.

Square both sides of the equation:

Subtract 2x from and add 5 to both sides of the equation.

Simplify.

There are no real solutions.

You can 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. Since there are no x-intercepts, there is no real solution to the equation.

If you would like to work another example, click on Example.

If you would like to test yourself by working some problems similar to this example, click on Problem.

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[Geometry] [Differential Equations]
[Calculus] [Complex Variables] [Matrix Algebra]