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Answer :
Sure! Let's solve the equation step by step:
1. Start with the given equation:
[tex]\[
27x^2 = 91
\][/tex]
2. Isolate [tex]\(x^2\)[/tex] by dividing both sides of the equation by 27:
[tex]\[
x^2 = \frac{91}{27}
\][/tex]
3. Simplify the fraction:
Since 91 and 27 do not share any common factors other than 1, we cannot reduce the fraction further. So,
[tex]\[
x^2 = \frac{91}{27}
\][/tex]
4. Find the value of [tex]\(x\)[/tex] by taking the square root of both sides:
There are typically two solutions for [tex]\(x\)[/tex] because both a positive and a negative number squared give the same result. So,
[tex]\[
x = \sqrt{\frac{91}{27}} \quad \text{and} \quad x = -\sqrt{\frac{91}{27}}
\][/tex]
5. Calculate the approximate numerical value:
When you calculate the square root, you'll find the approximate values for [tex]\(x\)[/tex]:
[tex]\[
x_1 \approx 1.8358
\][/tex]
[tex]\[
x_2 \approx -1.8358
\][/tex]
Therefore, the solutions for the equation [tex]\(27x^2 = 91\)[/tex] are approximately [tex]\(x \approx 1.8358\)[/tex] and [tex]\(x \approx -1.8358\)[/tex].
1. Start with the given equation:
[tex]\[
27x^2 = 91
\][/tex]
2. Isolate [tex]\(x^2\)[/tex] by dividing both sides of the equation by 27:
[tex]\[
x^2 = \frac{91}{27}
\][/tex]
3. Simplify the fraction:
Since 91 and 27 do not share any common factors other than 1, we cannot reduce the fraction further. So,
[tex]\[
x^2 = \frac{91}{27}
\][/tex]
4. Find the value of [tex]\(x\)[/tex] by taking the square root of both sides:
There are typically two solutions for [tex]\(x\)[/tex] because both a positive and a negative number squared give the same result. So,
[tex]\[
x = \sqrt{\frac{91}{27}} \quad \text{and} \quad x = -\sqrt{\frac{91}{27}}
\][/tex]
5. Calculate the approximate numerical value:
When you calculate the square root, you'll find the approximate values for [tex]\(x\)[/tex]:
[tex]\[
x_1 \approx 1.8358
\][/tex]
[tex]\[
x_2 \approx -1.8358
\][/tex]
Therefore, the solutions for the equation [tex]\(27x^2 = 91\)[/tex] are approximately [tex]\(x \approx 1.8358\)[/tex] and [tex]\(x \approx -1.8358\)[/tex].
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