Solve A=(3x-1)^2-16

$$A = ( 3 x - 1 ) ^ { 2 } - 16$$

Solve for A

$$A=3\left(3x-5\right)\left(x+1\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-1\right)^{2}.

$$A=9x^{2}-6x+1-16$$

Subtract 16 from 1 to get -15.

$$A=9x^{2}-6x-15$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{A+16}+1}{3}$$

$$x=\frac{\sqrt{A+16}+1}{3}$$

Solve for x

$$x=\frac{-\sqrt{A+16}+1}{3}$$

$$x=\frac{\sqrt{A+16}+1}{3}\text{, }A\geq -16$$