Solve x^4-32x^2-144=0

$$x ^ { 4 } - 32 x ^ { 2 } - 144 = 0$$

Solve for x (complex solution)

$$x=6$$

$$x=-6$$

$$x=-2i$$

$$x=2i$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}-32t-144=0$$

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, -32 for b, and -144 for c in the quadratic formula.

$$t=\frac{-\left(-32\right)±\sqrt{\left(-32\right)^{2}-4\times 1\left(-144\right)}}{2}$$

Do the calculations.

$$t=\frac{32±40}{2}$$

Solve the equation t=\frac{32±40}{2} when ± is plus and when ± is minus.

$$t=36 t=-4$$

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

$$x=-6 x=6 x=-2i x=2i$$

Solve for x

$$x=-6$$

$$x=6$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}-32t-144=0$$

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, -32 for b, and -144 for c in the quadratic formula.

$$t=\frac{-\left(-32\right)±\sqrt{\left(-32\right)^{2}-4\times 1\left(-144\right)}}{2}$$

Do the calculations.

$$t=\frac{32±40}{2}$$

Solve the equation t=\frac{32±40}{2} when ± is plus and when ± is minus.

$$t=36 t=-4$$

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

$$x=6 x=-6$$