Solution: First make a note of the fact that you cannot take the square root of a negative number. 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 . Multiply both sides of the equation by
Since is already isolated, 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 answers, one exact answer of 7 and one approximate answer of . 7.85207.
Check the solution 7 by substituting 7 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 7.85207 by substituting 7.85207 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-intercepts are 7 and 7.85207, we have verified the solution.
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