Solve 8b^4-36b^2+81=0

$$8 b ^ { 4 } - 36 b ^ { 2 } + 81 = 0$$

Solve for b

$$b=\frac{3\sqrt[4]{2}e^{\frac{7\pi i}{8}}}{2}\approx -1.64802617+0.682634791i$$

$$b=\frac{3\sqrt[4]{2}e^{\frac{15\pi i}{8}}}{2}\approx 1.64802617-0.682634791i$$

$$b=\frac{3\sqrt[4]{2}e^{\frac{9\pi i}{8}}}{2}\approx -1.64802617-0.682634791i$$

$$b=\frac{3\sqrt[4]{2}e^{\frac{\pi i}{8}}}{2}\approx 1.64802617+0.682634791i$$

Steps Using the Quadratic Formula

Substitute t for b^{2}.

$$8t^{2}-36t+81=0$$

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 8 for a, -36 for b, and 81 for c in the quadratic formula.

$$t=\frac{-\left(-36\right)±\sqrt{\left(-36\right)^{2}-4\times 8\times 81}}{2\times 8}$$

Do the calculations.

$$t=\frac{36±\sqrt{-1296}}{16}$$

Solve the equation t=\frac{36±\sqrt{-1296}}{16} when ± is plus and when ± is minus.

$$t=\frac{9}{4}+\frac{9}{4}i t=\frac{9}{4}-\frac{9}{4}i$$

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

$$b=-\frac{3\sqrt[4]{2}e^{\frac{\pi i}{8}}}{2} b=\frac{3\sqrt[4]{2}e^{\frac{\pi i}{8}}}{2} b=-\frac{\sqrt[4]{2}\times \left(3i\right)e^{\frac{3\pi i}{8}}}{2} b=\frac{\sqrt[4]{2}\times \left(3i\right)e^{\frac{3\pi i}{8}}}{2}$$