Sure, let's solve the equation together, step-by-step:
1. We start with the equation 5n² = 27.
2. The first step to solve this equation for n is to isolate n² by dividing each side of the equation by 5. So the equation becomes n² = 27 / 5.
3. After this step, the equation becomes n² = 5.4.
4. Then, we need to find the value of n. For that, we have to apply the square root to each side of the equation to cancel the square of n.
5. But there is something important to remember, the square root of a number can be positive or negative. This is because ¬(-n)² = n² = (-n)².
6. So when we solve this kind of equation, we will have two solutions. One is the positive square root, the other one is the negative square root.
7. Let's calculate. When we apply the square root to 5.4, we get the following numbers ±2.32379000772445.
This means that our solutions for n from the equation 5n² = 27 are n = 2.32379000772445 and n = -2.32379000772445.