Answer :

Sure, let's solve the equation [tex]\(4x^2 - 100 = 0\)[/tex] step by step.

1. Start with the given equation:
[tex]\[
4x^2 - 100 = 0
\][/tex]

2. Move the constant term [tex]\( -100 \)[/tex] to the right side of the equation by adding [tex]\(100\)[/tex] to both sides:
[tex]\[
4x^2 = 100
\][/tex]

3. Divide both sides of the equation by the coefficient of [tex]\(x^2\)[/tex], which is 4:
[tex]\[
x^2 = \frac{100}{4}
\][/tex]

4. Simplify the right side:
[tex]\[
x^2 = 25
\][/tex]

5. To solve for [tex]\(x\)[/tex], take the square root of both sides of the equation:
[tex]\[
x = \pm \sqrt{25}
\][/tex]

6. Simplify the square root:
[tex]\[
\sqrt{25} = 5
\][/tex]

So the solutions to the equation are:
[tex]\[
x = 5 \quad \text{and} \quad x = -5
\][/tex]

Thus, the correct answer is:
[tex]\[
\boxed{C. -5 \text{ and } 5}
\][/tex]

Thanks for taking the time to read If tex 4x 2 100 0 tex the roots of the equation are A 25 and 25 B 25 only C 5 and 5 D. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada