Note:
Example 4:
First make a note of the fact that you cannot take the square root of a negative number. Therefore, the term is valid only if the term is valid if , and the term is valid only if The equation is valid if all three terms are valid, therefore the domain is restricted to the common domain of the three terms or the set of real numbers
Square both sides of the equation and simplify.
Isolate the
term.
Square both sides of the equation and
simplify.
Use the quadratic formula to solve for x.
The answers are 15 and-0.078534.
Check the solution by substituting 15 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 15 for x, then x=15 is a solution.
Check the solution by substituting -0.078534 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 does not equal the right side of the original equation after we substituted -0.078534 for x, then x=-0.078534 is not a real solution.
You can also 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. The x-intercept(s) of this graph is(are) the solution(s). Since there is just one x-intercept at 15, then the only solution is x=15.
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