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Answer :
To solve the equation [tex]\(x^2 = \frac{1}{25}\)[/tex], follow these steps:
1. Understand the Equation: The equation [tex]\(x^2 = \frac{1}{25}\)[/tex] means we need to find the values of [tex]\(x\)[/tex] such that when [tex]\(x\)[/tex] is squared, it equals [tex]\(\frac{1}{25}\)[/tex].
2. Take the Square Root of Both Sides: To solve for [tex]\(x\)[/tex], take the square root of both sides of the equation. Remember that squaring a positive number or its negative counterpart yields the same result. Hence:
[tex]\[
x = \sqrt{\frac{1}{25}} \quad \text{or} \quad x = -\sqrt{\frac{1}{25}}
\][/tex]
3. Calculate the Square Root:
- The square root of [tex]\(\frac{1}{25}\)[/tex] is calculated as follows:
[tex]\[
\sqrt{\frac{1}{25}} = \frac{\sqrt{1}}{\sqrt{25}} = \frac{1}{5} = 0.2
\][/tex]
- Therefore, the possible values for [tex]\(x\)[/tex] are:
[tex]\[
x = 0.2 \quad \text{or} \quad x = -0.2
\][/tex]
4. Conclusion:
- The solutions to the equation [tex]\(x^2 = \frac{1}{25}\)[/tex] are [tex]\(x = 0.2\)[/tex] and [tex]\(x = -0.2\)[/tex].
This step-by-step process gives us the correct solutions for the given quadratic equation.
1. Understand the Equation: The equation [tex]\(x^2 = \frac{1}{25}\)[/tex] means we need to find the values of [tex]\(x\)[/tex] such that when [tex]\(x\)[/tex] is squared, it equals [tex]\(\frac{1}{25}\)[/tex].
2. Take the Square Root of Both Sides: To solve for [tex]\(x\)[/tex], take the square root of both sides of the equation. Remember that squaring a positive number or its negative counterpart yields the same result. Hence:
[tex]\[
x = \sqrt{\frac{1}{25}} \quad \text{or} \quad x = -\sqrt{\frac{1}{25}}
\][/tex]
3. Calculate the Square Root:
- The square root of [tex]\(\frac{1}{25}\)[/tex] is calculated as follows:
[tex]\[
\sqrt{\frac{1}{25}} = \frac{\sqrt{1}}{\sqrt{25}} = \frac{1}{5} = 0.2
\][/tex]
- Therefore, the possible values for [tex]\(x\)[/tex] are:
[tex]\[
x = 0.2 \quad \text{or} \quad x = -0.2
\][/tex]
4. Conclusion:
- The solutions to the equation [tex]\(x^2 = \frac{1}{25}\)[/tex] are [tex]\(x = 0.2\)[/tex] and [tex]\(x = -0.2\)[/tex].
This step-by-step process gives us the correct solutions for the given quadratic equation.
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