7) \( x^{4}+7 x^{2}=18 \)

To solve the equation \( x^{4}+7 x^{2}=18 \), you can start by performing a substitution. Let \( y = x^{2} \), which transforms the equation into \( y^{2} + 7y - 18 = 0 \). This is a quadratic equation that can be solved using the quadratic formula \( y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \). Plugging in \( a = 1, b = 7, c = -18 \), you'll find the roots for \( y \), and subsequently, if \( y \geq 0 \), you can find the corresponding values of \( x \) by taking the square root of \( y \). After completing the calculation, you'll have \( y = 2 \) and \( y = -9 \). Since \( y = -9 \) is not a valid solution for \( x^{2} \), you can take the square root of \( y = 2 \) to find \( x \). So, the solutions are \( x = \sqrt{2} \) and \( x = -\sqrt{2} \). Happy solving!