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.

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

Do the calculations.

$$t=\frac{-7±1}{-2}$$

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

$$t=3 t=4$$

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

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