Note:

- In order to solve for x, you must isolate x.
- In order to isolate x, you must remove it from under the radial.
- 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.

Problem2.6c:

Solution:

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

Rewrite the radical terms as exponential terms

Raise both sides of the equation to the power 8 and simplify.

Solve using the quadratic formula.

The answers are 2.804248 (rounded) and 0.445752 (rounded).

Check the solution by substituting 2.804248 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.

- Left side:
- Right side:

Since the solution *x*=0.445752 is not (the
domain), it cannot be a solution. However, if you forgot this fact,
you can discover the same thing by checking the equation.

Check the solution by substituting 0.445752 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.

- Left side:
- Right side:

You can also check the answer by graphing the equation:

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

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