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Answer :
To solve the equation [tex]\(25x^2 - 100 = 0\)[/tex], follow these steps:
1. Isolate the quadratic term:
Start with the given equation:
[tex]\[
25x^2 - 100 = 0
\][/tex]
Add 100 to both sides to move the constant term to the right side:
[tex]\[
25x^2 = 100
\][/tex]
2. Solve for [tex]\(x^2\)[/tex]:
Divide both sides by 25 to isolate [tex]\(x^2\)[/tex]:
[tex]\[
x^2 = \frac{100}{25}
\][/tex]
Simplifying the right side gives:
[tex]\[
x^2 = 4
\][/tex]
3. Find the square roots:
To solve for [tex]\(x\)[/tex], take the square root of both sides. Remember that there are two square roots for any positive number:
[tex]\[
x = \sqrt{4} \quad \text{or} \quad x = -\sqrt{4}
\][/tex]
4. Calculate the values:
The square root of 4 is 2. So, the solutions are:
[tex]\[
x = 2 \quad \text{or} \quad x = -2
\][/tex]
Thus, the solutions to the equation [tex]\(25x^2 - 100 = 0\)[/tex] are [tex]\(x = 2\)[/tex] and [tex]\(x = -2\)[/tex].
1. Isolate the quadratic term:
Start with the given equation:
[tex]\[
25x^2 - 100 = 0
\][/tex]
Add 100 to both sides to move the constant term to the right side:
[tex]\[
25x^2 = 100
\][/tex]
2. Solve for [tex]\(x^2\)[/tex]:
Divide both sides by 25 to isolate [tex]\(x^2\)[/tex]:
[tex]\[
x^2 = \frac{100}{25}
\][/tex]
Simplifying the right side gives:
[tex]\[
x^2 = 4
\][/tex]
3. Find the square roots:
To solve for [tex]\(x\)[/tex], take the square root of both sides. Remember that there are two square roots for any positive number:
[tex]\[
x = \sqrt{4} \quad \text{or} \quad x = -\sqrt{4}
\][/tex]
4. Calculate the values:
The square root of 4 is 2. So, the solutions are:
[tex]\[
x = 2 \quad \text{or} \quad x = -2
\][/tex]
Thus, the solutions to the equation [tex]\(25x^2 - 100 = 0\)[/tex] are [tex]\(x = 2\)[/tex] and [tex]\(x = -2\)[/tex].
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