Solve 2b^4-3b^2-2=0

$$2 b ^ { 4 } - 3 b ^ { 2 } - 2 = 0$$

Solve for b

$$b=-\sqrt{2}\approx -1.414213562$$

$$b=\sqrt{2}\approx 1.414213562$$

Steps Using the Quadratic Formula

Substitute t for b^{2}.

$$2t^{2}-3t-2=0$$

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 2 for a, -3 for b, and -2 for c in the quadratic formula.

$$t=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times 2\left(-2\right)}}{2\times 2}$$

Do the calculations.

$$t=\frac{3±5}{4}$$

Solve the equation t=\frac{3±5}{4} when ± is plus and when ± is minus.

$$t=2 t=-\frac{1}{2}$$

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

$$b=\sqrt{2} b=-\sqrt{2}$$