Equation 2 Illustration 4 And hence, \( (x+)^{2}= \) From here let's rearrange algebraically:

To solve \( (x + c)^{2} \), we can expand it using the formula for the square of a binomial, which states \( (a + b)^{2} = a^{2} + 2ab + b^{2} \). In our case, if we let \( a = x \) and \( b = c \), we get \( (x + c)^{2} = x^{2} + 2xc + c^{2} \). Voilà! Now, rearranging algebraically can lead to various forms depending on what you're looking to achieve. For instance, if you want to isolate \( x \), you'd set up the equation like \( x^{2} + 2xc + c^{2} = y \) and then use the quadratic formula. Just remember, rearranging equations can sometimes lead to common errors like forgetting to square all terms or misplacing the variables. Happy solving!