Answer :

Sure! Let's solve the equation [tex]\( y = 25x^2 - 100 \)[/tex] step-by-step, specifically looking to find the values of [tex]\( x \)[/tex] when [tex]\( y = 0 \)[/tex].

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

2. Set [tex]\( y = 0 \)[/tex] to find the roots (solutions) of the equation:
[tex]\[
0 = 25x^2 - 100
\][/tex]

3. Add 100 to both sides to isolate the quadratic term:
[tex]\[
25x^2 = 100
\][/tex]

4. Divide both sides by 25 to solve for [tex]\( x^2 \)[/tex]:
[tex]\[
x^2 = \frac{100}{25}
\][/tex]

5. Simplify the fraction:
[tex]\[
x^2 = 4
\][/tex]

6. To find [tex]\( x \)[/tex], take the square root of both sides. Remember, there are two possible square roots for a positive number:
[tex]\[
x = \pm \sqrt{4}
\][/tex]

7. Simplify the square root:
[tex]\[
x = \pm 2
\][/tex]

So, the solutions for [tex]\( x \)[/tex] are [tex]\( x = 2 \)[/tex] and [tex]\( x = -2 \)[/tex]. These are the values of [tex]\( x \)[/tex] that satisfy the equation when [tex]\( y = 0 \)[/tex].

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Rewritten by : Barada