Solve x^4-7x^2+12=0

$$x ^ { 4 } - 7 x ^ { 2 } + 12 = 0$$

Solve for x

$$x=-2$$

$$x=2$$

$$x=\sqrt{3}\approx 1.732050808$$

$$x=-\sqrt{3}\approx -1.732050808$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}-7t+12=0$$

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, -7 for b, and 12 for c in the quadratic formula.

$$t=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\times 1\times 12}}{2}$$

Do the calculations.

$$t=\frac{7±1}{2}$$

Solve the equation t=\frac{7±1}{2} when ± is plus and when ± is minus.

$$t=4 t=3$$

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

$$x=2 x=-2 x=\sqrt{3} x=-\sqrt{3}$$