Question

1. $5n^2 + 3 = 248$

Explanation:

Step1: Subtract 3 from both sides

To isolate the term with \( n^2 \), we subtract 3 from both sides of the equation \( 5n^2 + 3 = 248 \). This gives us \( 5n^2 = 248 - 3 \). Calculating the right side, we have \( 5n^2 = 245 \).

Step2: Divide both sides by 5

Next, we divide both sides of the equation \( 5n^2 = 245 \) by 5 to solve for \( n^2 \). This results in \( n^2=\frac{245}{5} \), and simplifying the right side gives \( n^2 = 49 \).

Step3: Take square root of both sides

To find the value of \( n \), we take the square root of both sides of the equation \( n^2 = 49 \). Remembering that the square root of a number has two solutions (positive and negative), we get \( n=\pm\sqrt{49} \), which simplifies to \( n = \pm 7 \).

Answer:

\( n = 7 \) or \( n = -7 \)