Solve A=(3x-2)^2-2

$$A = ( 3 x - 2 ) ^ { 2 } - 2$$

Solve for A

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-2\right)^{2}.

$$A=9x^{2}-12x+4-2$$

Subtract 2 from 4 to get 2.

$$A=9x^{2}-12x+2$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{A+2}+2}{3}$$

$$x=\frac{\sqrt{A+2}+2}{3}$$

Solve for x

$$x=\frac{-\sqrt{A+2}+2}{3}$$

$$x=\frac{\sqrt{A+2}+2}{3}\text{, }A\geq -2$$