Note:
Example 5:
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 and the term is valid if . The restricted domain must satisfy both of these constraints. Therefore, the domain is the set of real numbers
Isolate the term by adding 3 to both sides
of the equation.
Square both sides of the equation.
Isolate the term.
Square both sides of the equation.
Solve for x using the quadratic formula.
There are two approximate answers, 8163.162 and 18.8385.
Check the solution 8163.162 by substituting 8163.162 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.
Check the solution 18.8385 by substituting 18.8385 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:
.
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 the x-intercept is 8163.162, we have verified the solution.
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Author:Nancy Marcus