Solve x^4-15x^2=16

$${ x }^{ 4 } -15 { x }^{ 2 } =16$$

Solve for x (complex solution)

$$x=4$$

$$x=-4$$

$$x=-i$$

$$x=i$$

Steps Using the Quadratic Formula

Subtract 16 from both sides.

$$x^{4}-15x^{2}-16=0$$

Substitute t for x^{2}.

$$t^{2}-15t-16=0$$

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, -15 for b, and -16 for c in the quadratic formula.

$$t=\frac{-\left(-15\right)±\sqrt{\left(-15\right)^{2}-4\times 1\left(-16\right)}}{2}$$

Do the calculations.

$$t=\frac{15±17}{2}$$

Solve the equation t=\frac{15±17}{2} when ± is plus and when ± is minus.

$$t=16 t=-1$$

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

$$x=-4 x=4 x=-i x=i$$

Solve for x

$$x=-4$$

$$x=4$$

Steps Using the Quadratic Formula

Subtract 16 from both sides.

$$x^{4}-15x^{2}-16=0$$

Substitute t for x^{2}.

$$t^{2}-15t-16=0$$

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, -15 for b, and -16 for c in the quadratic formula.

$$t=\frac{-\left(-15\right)±\sqrt{\left(-15\right)^{2}-4\times 1\left(-16\right)}}{2}$$

Do the calculations.

$$t=\frac{15±17}{2}$$

Solve the equation t=\frac{15±17}{2} when ± is plus and when ± is minus.

$$t=16 t=-1$$

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

$$x=4 x=-4$$