Solve -40-5b^2+b^4=0

$$- 40 - 5 b ^ { 2 } + b ^ { 4 } = 0$$

Solve for b

$$b = -\frac{\sqrt{2 {(\sqrt{185} + 5)}}}{2} \approx -3.049710684$$

$$b = \frac{\sqrt{2 {(\sqrt{185} + 5)}}}{2} \approx 3.049710684$$

Steps Using the Quadratic Formula

Substitute t for b^{2}.

$$t^{2}-5t-40=0$$

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 1 for a, -5 for b, and -40 for c in the quadratic formula.

$$t=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 1\left(-40\right)}}{2}$$

Do the calculations.

$$t=\frac{5±\sqrt{185}}{2}$$

Solve the equation t=\frac{5±\sqrt{185}}{2} when ± is plus and when ± is minus.

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

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

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