Solve x^4-10x^2+24=0

$$x ^ { 4 } - 10 x ^ { 2 } + 24 = 0$$

Solve for x

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

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

$$x=2$$

$$x=-2$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}-10t+24=0$$

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, -10 for b, and 24 for c in the quadratic formula.

$$t=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\times 1\times 24}}{2}$$

Do the calculations.

$$t=\frac{10±2}{2}$$

Solve the equation t=\frac{10±2}{2} when ± is plus and when ± is minus.

$$t=6 t=4$$

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

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