Solve a^4-8a^2=-12

$$a ^ { 4 } - 8 a ^ { 2 } = - 12$$

Solve for a

$$a=-\sqrt{6}\approx -2.449489743$$

$$a=\sqrt{6}\approx 2.449489743$$

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

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

Steps Using the Quadratic Formula

Add 12 to both sides.

$$a^{4}-8a^{2}+12=0$$

Substitute t for a^{2}.

$$t^{2}-8t+12=0$$

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, -8 for b, and 12 for c in the quadratic formula.

$$t=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 1\times 12}}{2}$$

Do the calculations.

$$t=\frac{8±4}{2}$$

Solve the equation t=\frac{8±4}{2} when ± is plus and when ± is minus.

$$t=6 t=2$$

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

$$a=\sqrt{6} a=-\sqrt{6} a=\sqrt{2} a=-\sqrt{2}$$