Example 2:
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 second 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
Multiply both sides of the equation by 3 to remove the fraction.
Square both sides of the equation and simplify.
Isolate the
term and simplify.
Square both sides of the equation and
simplify.
Use the quadratic formula to solve for x.
The answers are
Check the solution by substituting 5 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 5 for x, then x=5 is a solution.
Check the solution by substituting 0.155505 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 0.155505 for x, then the solution x=0.155505 is a not valid and not a solution after all.
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 5, then the only solution is x=5.
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Author:Nancy Marcus