Solve the equation. \[ x^{4}-4 x^{2}-60=0 \] The solution set is \( \} \). (Simplify your answer. Use commas tc

To solve the equation \( x^4 - 4x^2 - 60 = 0 \), we can use a substitution method. Let \( y = x^2 \). Then the equation becomes: \[ y^2 - 4y - 60 = 0 \] Now, we can factor or use the quadratic formula. The quadratic formula is given by: \[ y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] Here, \( a = 1 \), \( b = -4 \), and \( c = -60 \). Plugging in these values gives: \[ y = \frac{-(-4) \pm \sqrt{(-4)^2 - 4 \cdot 1 \cdot (-60)}}{2 \cdot 1} = \frac{4 \pm \sqrt{16 + 240}}{2} \] \[ y = \frac{4 \pm \sqrt{256}}{2} = \frac{4 \pm 16}{2} \] This yields two solutions for \( y \): 1. \( y = \frac{20}{2} = 10 \) 2. \( y = \frac{-12}{2} = -6 \) Since \( y = x^2 \) and must be non-negative, we discard \( y = -6 \) and keep \( y = 10 \). Now substitute back to find \( x \): \[ x^2 = 10 \] Taking the square root of both sides gives: \[ x = \sqrt{10} \text{ or } x = -\sqrt{10} \] Thus, the solution set is: \(\{-\sqrt{10}, \sqrt{10}\}\)