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What is the result of isolating [tex]$x^2$[/tex] in the equation below?

[tex]4x^2 + 25y^2 = 100[/tex]

A. [tex]x^2 = 100 - \frac{25}{4}y^3[/tex]

B. [tex]x^2 = 25 - \frac{25}{4}y^2[/tex]

C. [tex]y^2 = 100 - 4x^2[/tex]

D. [tex]y^2 = 4 - \frac{4}{25}x^2[/tex]

Answer :

To isolate [tex]\( x^2 \)[/tex] in the equation [tex]\( 4x^2 + 25y^2 = 100 \)[/tex], follow these steps:

1. Start with the original equation:
[tex]\[
4x^2 + 25y^2 = 100
\][/tex]

2. To isolate [tex]\( x^2 \)[/tex], subtract [tex]\( 25y^2 \)[/tex] from both sides of the equation:
[tex]\[
4x^2 = 100 - 25y^2
\][/tex]

3. Next, divide every term by 4 to solve for [tex]\( x^2 \)[/tex]:
[tex]\[
x^2 = \frac{100 - 25y^2}{4}
\][/tex]

Now let's simplify the result:

4. Simplify the expression [tex]\(\frac{100 - 25y^2}{4}\)[/tex]:

- Divide each term in the numerator by 4:
[tex]\[
x^2 = \frac{100}{4} - \frac{25y^2}{4}
\][/tex]

- Simplify further:
[tex]\[
x^2 = 25 - \frac{25y^2}{4}
\][/tex]

So, the result of isolating [tex]\( x^2 \)[/tex] is:
[tex]\[
x^2 = 25 - \frac{25y^2}{4}
\][/tex]

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