d) \( x-9 x^{\frac{1}{2}}+18=0 \)

To solve the equation \( x - 9 x^{\frac{1}{2}} + 18 = 0 \), let's first substitute \( y = x^{\frac{1}{2}} \). This means \( x = y^2 \), and the equation becomes: \[ y^2 - 9y + 18 = 0 \] Now, we can factor this quadratic equation: \[ (y - 6)(y - 3) = 0 \] This gives us \( y = 6 \) and \( y = 3 \). Returning to our original variable, we square these values: \[ x = 6^2 = 36 \quad \text{and} \quad x = 3^2 = 9 \] Therefore, the solutions to the original equation are \( x = 36 \) and \( x = 9 \). Got your calculator? Great! Because solving quadratics is like finding treasure—it’s all about the right formula or the perfect factorization. And remember, when you spot a square root, don't shy away! Embrace it and simplify your task to see the clear path to your solution!