Solve D^4+8D^2+16=0

$$D ^ { 4 } + 8 D ^ { 2 } + 16 = 0$$

Solve for D

$$D=-2i$$

$$D=2i$$

Steps Using the Quadratic Formula

Substitute t for D^{2}.

$$t^{2}+8t+16=0$$

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, 8 for b, and 16 for c in the quadratic formula.

$$t=\frac{-8±\sqrt{8^{2}-4\times 1\times 16}}{2}$$

Do the calculations.

$$t=\frac{-8±0}{2}$$

Solutions are the same.

$$t=-4$$

Since D=t^{2}, the solutions are obtained by solving the equation for each t.

$$D=2i D=-2i$$