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*.Problem2.2d:

Answer:

*x*=-59,042.Solution:

- Subtract 8 from both sides of the equation so that the radical term is
isolated.

- Multiply both sides of the equation by
*x*-7=-59,049 - Add 7 to both sides of the equation.
*x*=-59,042 - Check the answer by substituting -59,042 in the original equation for
*x*. If the left side of the equation equals the right side of the equationafter the substitution, you have found the correct answer.

Left side:

Right side: You can also check the answer by graphing

(the left side of the original equation minus the right side of the original

equation). The solution will be the x-intercept. The x-intercept (and

hence the solution) on the graph is -59,042.

If you would like to review the solution to Problem 2.2e, click here.

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

If you would like to go back to the equation table of contents, click

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**Author: Nancy Marcus**Copyright © 1999-2017 MathMedics, LLC. All rights reserved.

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