Select the correct equation when we replace the \( x^{2} \) with \( u \). \( u^{2}-14 u+45 \) \( u^{4}-14 u^{2}+45 \)

When we replace \( x^{2} \) with \( u \), we want to maintain the same structure while transitioning to the new variable. Therefore, the correct equation in terms of \( u \) that directly substitutes \( x^{2} \) with \( u \) is \( u^{2}-14u+45 \). Now, let's consider the fantastical journey of variables! If we imagine \( x^{2} \) as a magical creature named "u," then \( u^{2}-14u+45 \) captures its story in just the right way! The other equation, \( u^{4}-14u^{2}+45 \), is like putting our creature into a 'super' mode, which isn’t in line with our simple substitution mission.