At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Experience the ease of finding precise answers to your questions from a knowledgeable community of experts. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
Let's solve the equation step-by-step: [tex]\(\sqrt{2n + 28} - 4\sqrt{n} = 0\)[/tex].
1. We start with the given equation:
[tex]\[ \sqrt{2n + 28} - 4\sqrt{n} = 0 \][/tex]
2. To isolate [tex]\(\sqrt{2n + 28}\)[/tex], let’s make [tex]\(\sqrt{2n + 28}\)[/tex] equal to [tex]\(4\sqrt{n}\)[/tex]:
[tex]\[ \sqrt{2n + 28} = 4\sqrt{n} \][/tex]
3. Now, we square both sides of the equation to remove the square roots:
[tex]\[ (\sqrt{2n + 28})^2 = (4\sqrt{n})^2 \][/tex]
Simplifying this, we get:
[tex]\[ 2n + 28 = 16n \][/tex]
4. We need to solve for [tex]\(n\)[/tex]. Let’s isolate [tex]\(n\)[/tex] on one side of the equation:
[tex]\[ 2n + 28 = 16n \][/tex]
Subtract [tex]\(2n\)[/tex] from both sides:
[tex]\[ 28 = 14n \][/tex]
5. Finally, divide both sides by 14:
[tex]\[ n = \frac{28}{14} \][/tex]
[tex]\[ n = 2 \][/tex]
So, the solution to the equation [tex]\(\sqrt{2n + 28} - 4\sqrt{n} = 0\)[/tex] is [tex]\( n = 2 \)[/tex]. Therefore, from the given options, [tex]\( n = 2 \)[/tex] is the correct answer.
1. We start with the given equation:
[tex]\[ \sqrt{2n + 28} - 4\sqrt{n} = 0 \][/tex]
2. To isolate [tex]\(\sqrt{2n + 28}\)[/tex], let’s make [tex]\(\sqrt{2n + 28}\)[/tex] equal to [tex]\(4\sqrt{n}\)[/tex]:
[tex]\[ \sqrt{2n + 28} = 4\sqrt{n} \][/tex]
3. Now, we square both sides of the equation to remove the square roots:
[tex]\[ (\sqrt{2n + 28})^2 = (4\sqrt{n})^2 \][/tex]
Simplifying this, we get:
[tex]\[ 2n + 28 = 16n \][/tex]
4. We need to solve for [tex]\(n\)[/tex]. Let’s isolate [tex]\(n\)[/tex] on one side of the equation:
[tex]\[ 2n + 28 = 16n \][/tex]
Subtract [tex]\(2n\)[/tex] from both sides:
[tex]\[ 28 = 14n \][/tex]
5. Finally, divide both sides by 14:
[tex]\[ n = \frac{28}{14} \][/tex]
[tex]\[ n = 2 \][/tex]
So, the solution to the equation [tex]\(\sqrt{2n + 28} - 4\sqrt{n} = 0\)[/tex] is [tex]\( n = 2 \)[/tex]. Therefore, from the given options, [tex]\( n = 2 \)[/tex] is the correct answer.
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.