Solve 5b^4-15b^2+2=0

$$5 b ^ { 4 } - 15 b ^ { 2 } + 2 = 0$$

Solve for b

$$b=-\frac{\sqrt{150-10\sqrt{185}}}{10}\approx -0.373969182$$

$$b=\frac{\sqrt{150-10\sqrt{185}}}{10}\approx 0.373969182$$

$$b = \frac{\sqrt{10 \sqrt{185} + 150}}{10} \approx 1.691196928$$

$$b = -\frac{\sqrt{10 \sqrt{185} + 150}}{10} \approx -1.691196928$$

Steps Using the Quadratic Formula

Substitute t for b^{2}.

$$5t^{2}-15t+2=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 5 for a, -15 for b, and 2 for c in the quadratic formula.

$$t=\frac{-\left(-15\right)±\sqrt{\left(-15\right)^{2}-4\times 5\times 2}}{2\times 5}$$

Do the calculations.

$$t=\frac{15±\sqrt{185}}{10}$$

Solve the equation t=\frac{15±\sqrt{185}}{10} when ± is plus and when ± is minus.

$$t=\frac{\sqrt{185}}{10}+\frac{3}{2} t=-\frac{\sqrt{185}}{10}+\frac{3}{2}$$

Since b=t^{2}, the solutions are obtained by evaluating b=±\sqrt{t} for each t.

$$b=\frac{\sqrt{\frac{2\sqrt{185}}{5}+6}}{2} b=-\frac{\sqrt{\frac{2\sqrt{185}}{5}+6}}{2} b=\frac{\sqrt{-\frac{2\sqrt{185}}{5}+6}}{2} b=-\frac{\sqrt{-\frac{2\sqrt{185}}{5}+6}}{2}$$