Solve D=(4-x)^2-4

$$D = ( 4 - x ) ^ { 2 } - 4$$

Solve for D

$$D=\left(x-6\right)\left(x-2\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4-x\right)^{2}.

$$D=16-8x+x^{2}-4$$

Subtract 4 from 16 to get 12.

$$D=12-8x+x^{2}$$

Solve for x (complex solution)

$$x=\sqrt{D+4}+4$$

$$x=-\sqrt{D+4}+4$$

Solve for x

$$x=\sqrt{D+4}+4$$

$$x=-\sqrt{D+4}+4\text{, }D\geq -4$$