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Answer :
We are given the equation
$$
4x^2 - 100 = 0.
$$
**Step 1: Divide by 4**
Since 4 is a non-zero constant, we can divide the equation by 4:
$$
x^2 - 25 = 0.
$$
**Step 2: Recognize the Difference of Squares**
Notice that $x^2 - 25$ is a difference of squares because $25 = 5^2$. Recall the identity:
$$
a^2 - b^2 = (a - b)(a + b).
$$
Thus, we can write:
$$
x^2 - 25 = (x - 5)(x + 5).
$$
**Step 3: Solve for $x$**
For the product to be zero, either factor must be zero:
\[
\begin{aligned}
x - 5 &= 0 \quad \Rightarrow \quad x = 5, \\
x + 5 &= 0 \quad \Rightarrow \quad x = -5.
\end{aligned}
\]
**Conclusion**
The roots of the equation are $x = -5$ and $x = 5$.
Thus, the correct answer is option 3) \(-5\) and \(5\).
$$
4x^2 - 100 = 0.
$$
**Step 1: Divide by 4**
Since 4 is a non-zero constant, we can divide the equation by 4:
$$
x^2 - 25 = 0.
$$
**Step 2: Recognize the Difference of Squares**
Notice that $x^2 - 25$ is a difference of squares because $25 = 5^2$. Recall the identity:
$$
a^2 - b^2 = (a - b)(a + b).
$$
Thus, we can write:
$$
x^2 - 25 = (x - 5)(x + 5).
$$
**Step 3: Solve for $x$**
For the product to be zero, either factor must be zero:
\[
\begin{aligned}
x - 5 &= 0 \quad \Rightarrow \quad x = 5, \\
x + 5 &= 0 \quad \Rightarrow \quad x = -5.
\end{aligned}
\]
**Conclusion**
The roots of the equation are $x = -5$ and $x = 5$.
Thus, the correct answer is option 3) \(-5\) and \(5\).
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