Solve x^4+14x^2-72=0

$$x ^ { 4 } + 14 x ^ { 2 } - 72 = 0$$

Solve for x (complex solution)

$$x=2$$

$$x=-2$$

$$x=-3\sqrt{2}i\approx -0-4.242640687i$$

$$x=3\sqrt{2}i\approx 4.242640687i$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}+14t-72=0$$

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, 14 for b, and -72 for c in the quadratic formula.

$$t=\frac{-14±\sqrt{14^{2}-4\times 1\left(-72\right)}}{2}$$

Do the calculations.

$$t=\frac{-14±22}{2}$$

Solve the equation t=\frac{-14±22}{2} when ± is plus and when ± is minus.

$$t=4 t=-18$$

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

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

Solve for x

$$x=-2$$

$$x=2$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}+14t-72=0$$

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, 14 for b, and -72 for c in the quadratic formula.

$$t=\frac{-14±\sqrt{14^{2}-4\times 1\left(-72\right)}}{2}$$

Do the calculations.

$$t=\frac{-14±22}{2}$$

Solve the equation t=\frac{-14±22}{2} when ± is plus and when ± is minus.

$$t=4 t=-18$$

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

$$x=2 x=-2$$