To solve the equation [tex]\( x^2 = \frac{25}{36} \)[/tex], let's follow the steps:
1. Understand the Equation: The equation [tex]\( x^2 = \frac{25}{36} \)[/tex] indicates that [tex]\( x \)[/tex] squared is equal to the fraction [tex]\( \frac{25}{36} \)[/tex].
2. Take the Square Root: To find the values of [tex]\( x \)[/tex], we need to take the square root of both sides of the equation. Recall that taking the square root will give us both the positive and negative roots:
[tex]\[
x = \pm \sqrt{\frac{25}{36}}
\][/tex]
3. Simplify the Square Root: Simplify the square root of the fraction. We can do this by taking the square root of the numerator and the denominator separately:
[tex]\[
\sqrt{\frac{25}{36}} = \frac{\sqrt{25}}{\sqrt{36}} = \frac{5}{6}
\][/tex]
Therefore:
[tex]\[
x = \pm \frac{5}{6}
\][/tex]
4. Identify the Solutions: The solutions to the equation [tex]\( x^2 = \frac{25}{36} \)[/tex] are:
[tex]\[
x = \frac{5}{6} \quad \text{and} \quad x = -\frac{5}{6}
\][/tex]
Given these solutions, we can identify the correct answers from the provided choices:
- 6
- [tex]$-5$[/tex]
- [tex]$-6$[/tex]
- [tex]$\frac{5}{6}$[/tex]
- [tex]$-\frac{5}{6}$[/tex]
- 5
The correct choices are:
[tex]\[
\frac{5}{6} \quad \text{and} \quad -\frac{5}{6}
\][/tex]
