To find the solution(s) for the equation [tex]\( x^2 = \frac{100}{361} \)[/tex], follow these steps:
1. Write down the given equation:
[tex]\[ x^2 = \frac{100}{361} \][/tex]
2. Take the square root of both sides:
To solve for [tex]\( x \)[/tex], we need to take the square root of both sides of the equation. Remember that taking the square root will result in two values: one positive and one negative.
[tex]\[ x = \pm \sqrt{\frac{100}{361}} \][/tex]
3. Simplify the square root:
[tex]\[ x = \pm \frac{\sqrt{100}}{\sqrt{361}} \][/tex]
We know that [tex]\(\sqrt{100} = 10\)[/tex] and [tex]\(\sqrt{361} = 19\)[/tex]:
[tex]\[ x = \pm \frac{10}{19} \][/tex]
So, the solutions are:
[tex]\[ x = \frac{10}{19} \quad \text{and} \quad x = -\frac{10}{19} \][/tex]
4. Match with the given choices:
Let's compare our solutions with the provided options:
A) [tex]\( x = -\frac{10}{9} \)[/tex]
This value is incorrect as it does not match [tex]\(-\frac{10}{19}\)[/tex].
B) [tex]\( x = -\frac{1}{6} \)[/tex]
This value is incorrect as it does not match [tex]\(-\frac{10}{19}\)[/tex].
C) [tex]\( x = \frac{5}{18} \)[/tex]
This value is incorrect as it does not match [tex]\(\frac{10}{19}\)[/tex].
D) [tex]\( x = \frac{5}{9} \)[/tex]
This value is incorrect as it does not match [tex]\(\frac{10}{19}\)[/tex].
[tex]\( \text{None of the above} \)[/tex]
This choice implies that none of the listed options are correct.
Since none of the provided choices (A, B, C, D) match our correct solutions of [tex]\( x = \pm \frac{10}{19} \)[/tex], the final answer is:
[tex]\[
\boxed{\text{None of the above}}
\][/tex]
