Question

1. $n^2 - 24 = -2n$

Explanation:

Step1: Rearrange the equation

We start with the equation \( n^2 - 24 = -2n \). To solve a quadratic equation, we want it in standard form \( ax^2 + bx + c = 0 \). So we add \( 2n \) to both sides to get \( n^2 + 2n - 24 = 0 \).

Step2: Factor the quadratic

We need two numbers that multiply to \( -24 \) and add to \( 2 \). The numbers are \( 6 \) and \( -4 \) because \( 6 \times (-4) = -24 \) and \( 6 + (-4) = 2 \). So we can factor the quadratic as \( (n + 6)(n - 4) = 0 \).

Step3: Solve for n

Using the zero - product property, if \( (n + 6)(n - 4)=0 \), then either \( n + 6 = 0 \) or \( n - 4 = 0 \).

• If \( n+6 = 0 \), then \( n=-6 \).
• If \( n - 4=0 \), then \( n = 4 \).

Answer:

\( n=-6 \) or \( n = 4 \)