Solve x^4-24x^2+144=0

$$x ^ { 4 } - 24 x ^ { 2 } + 144 = 0$$

Solve for x

$$x=2\sqrt{3}\approx 3.464101615$$

$$x=-2\sqrt{3}\approx -3.464101615$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}-24t+144=0$$

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, -24 for b, and 144 for c in the quadratic formula.

$$t=\frac{-\left(-24\right)±\sqrt{\left(-24\right)^{2}-4\times 1\times 144}}{2}$$

Do the calculations.

$$t=\frac{24±0}{2}$$

Solutions are the same.

$$t=12$$

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

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