Solve, \( 10 x^{4}-19 x^{2}+6=0 \) The solution set is \( \{ \). (Type exact answers, using radicals as needed. Use a comma to sepa

To solve the equation \( 10 x^{4}-19 x^{2}+6=0 \), we can make a substitution. Let \( y = x^2 \). Thus, the equation becomes: \[ 10y^2 - 19y + 6 = 0 \] Next, we can apply the quadratic formula, \( y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 10 \), \( b = -19 \), and \( c = 6 \). Calculating the discriminant: \[ b^2 - 4ac = (-19)^2 - 4(10)(6) = 361 - 240 = 121 \] Now substituting into the quadratic formula: \[ y = \frac{19 \pm \sqrt{121}}{2 \cdot 10} = \frac{19 \pm 11}{20} \] This gives us two values for \( y \): \[ y_1 = \frac{30}{20} = \frac{3}{2} \] \[ y_2 = \frac{8}{20} = \frac{2}{5} \] Now, we substitute back to find \( x^2 \): 1. For \( x^2 = \frac{3}{2} \): \[ x = \pm \sqrt{\frac{3}{2}} = \pm \frac{\sqrt{6}}{2} \] 2. For \( x^2 = \frac{2}{5} \): \[ x = \pm \sqrt{\frac{2}{5}} = \pm \frac{\sqrt{10}}{5} \] Thus, the solution set is: \[ \left\{ \frac{\sqrt{6}}{2}, -\frac{\sqrt{6}}{2}, \frac{\sqrt{10}}{5}, -\frac{\sqrt{10}}{5} \right\} \]