Solve D=(3x+8)(3x-8)

$$D = ( 3 x + 8 ) ( 3 x - 8 )$$

Solve for D

$$D=9x^{2}-64$$

Solution Steps

Consider \left(3x+8\right)\left(3x-8\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 8.

$$D=\left(3x\right)^{2}-64$$

Expand \left(3x\right)^{2}.

$$D=3^{2}x^{2}-64$$

Calculate 3 to the power of 2 and get 9.

$$D=9x^{2}-64$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{D+64}}{3}$$

$$x=\frac{\sqrt{D+64}}{3}$$

Solve for x

$$x=-\frac{\sqrt{D+64}}{3}$$

$$x=\frac{\sqrt{D+64}}{3}\text{, }D\geq -64$$