To determine the value(s) of [tex]\( x \)[/tex] for which the equation [tex]\(\sqrt{x} = -7\)[/tex] is true, let's analyze the properties of the square root function.
1. By definition, the square root of a number always results in a non-negative value. This means [tex]\(\sqrt{x} \geq 0\)[/tex] for any real number [tex]\( x \)[/tex].
2. Given the equation [tex]\(\sqrt{x} = -7\)[/tex], we need to evaluate if it is possible for this equation to hold true.
- Since [tex]\(\sqrt{x}\)[/tex] is always non-negative, it cannot be equal to a negative number.
- Therefore, [tex]\(\sqrt{x} = -7\)[/tex] is inherently contradictory because [tex]\(-7\)[/tex] is negative and the square root function cannot yield a negative result.
3. Based on the properties outlined for the square root, there is no real number [tex]\( x \)[/tex] that would satisfy the equation [tex]\(\sqrt{x} = -7\)[/tex].
4. Consequently, the equation [tex]\(\sqrt{x} = -7\)[/tex] has no solution.
Therefore, the correct answer is:
(D) None of the above
