Note:
Example 3:
First make a note of the fact that you cannot take the square root of a negative number. Therefore,the first term is valid only if and the second term is valid if . Therefore, the domain is restricted to the set of real numbers x, .
Isolate the term
Square both sides of the equation.
Isolate the term.
Square both sides of the equation.
Solve for x using the quadratic formula.
There is one exact answer of 4 and one approximate answer of -1.387755.
Check the solution 4 by substituting 4 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.
Since the left side of the original equation equals the right side of the original equation after we substituted our solution for x, we have verified that the solutions is x=4.
Check the solution -1.387755 by substituting -1.387755 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.
You can also check the answer by graphing the equation:
If you would like to test yourself by working some problems similar to this example, click on Problem.
If you would like to go back to the equation table of contents, click on Contents.
Do you need more help? Please post your question on our S.O.S. Mathematics CyberBoard.
Author:Nancy Marcus