Solve A=(x-4)^2-x+2(3x-1)

$$A = ( x - 4 ) ^ { 2 } - x + 2 ( 3 x - 1 )$$

Solve for A

$$A=x^{2}-3x+14$$

Solution Steps

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

$$A=x^{2}-8x+16-x+2\left(3x-1\right)$$

Combine -8x and -x to get -9x.

$$A=x^{2}-9x+16+2\left(3x-1\right)$$

Use the distributive property to multiply 2 by 3x-1.

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

Combine -9x and 6x to get -3x.

$$A=x^{2}-3x+16-2$$

Subtract 2 from 16 to get 14.

$$A=x^{2}-3x+14$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{4A-47}+3}{2}$$

$$x=\frac{\sqrt{4A-47}+3}{2}$$

Solve for x

$$x=\frac{-\sqrt{4A-47}+3}{2}$$

$$x=\frac{\sqrt{4A-47}+3}{2}\text{, }A\geq \frac{47}{4}$$