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 3:

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

Square both sides of the equation.

Subtract 15 from both sides of the equation

Multiply both sides of the equation by

The answer is x = -16.5

Check the solution by substituting -16.5 in the original equation for x. If the left side of the equation equals the right side of the equation after the substitution, you have found the correct answer.

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