Solve x^4+14x^2-32=0

$$x ^ { 4 } + 14 x ^ { 2 } - 32 = 0$$

Solve for x (complex solution)

$$x=\sqrt{2}\approx 1.414213562$$

$$x=-\sqrt{2}\approx -1.414213562$$

$$x=-4i$$

$$x=4i$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}+14t-32=0$$

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 -32 for c in the quadratic formula.

$$t=\frac{-14±\sqrt{14^{2}-4\times 1\left(-32\right)}}{2}$$

Do the calculations.

$$t=\frac{-14±18}{2}$$

Solve the equation t=\frac{-14±18}{2} when ± is plus and when ± is minus.

$$t=2 t=-16$$

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

$$x=-\sqrt{2} x=\sqrt{2} x=-4i x=4i$$

Solve for x

$$x=-\sqrt{2}\approx -1.414213562$$

$$x=\sqrt{2}\approx 1.414213562$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}+14t-32=0$$

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 -32 for c in the quadratic formula.

$$t=\frac{-14±\sqrt{14^{2}-4\times 1\left(-32\right)}}{2}$$

Do the calculations.

$$t=\frac{-14±18}{2}$$

Solve the equation t=\frac{-14±18}{2} when ± is plus and when ± is minus.

$$t=2 t=-16$$

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

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