Solve A=16x^2-8x+1+left(5-6xright)left(4x-1right)

$$A = 16 { x }^{ 2 } -8x+1+ \left( 5-6x \right) \left( 4x-1 \right)$$

Solve for A

$$A=-2\left(x-2\right)\left(4x-1\right)$$

Solution Steps

Use the distributive property to multiply 5-6x by 4x-1 and combine like terms.

$$A=16x^{2}-8x+1+26x-5-24x^{2}$$

Combine -8x and 26x to get 18x.

$$A=16x^{2}+18x+1-5-24x^{2}$$

Subtract 5 from 1 to get -4.

$$A=16x^{2}+18x-4-24x^{2}$$

Combine 16x^{2} and -24x^{2} to get -8x^{2}.

$$A=-8x^{2}+18x-4$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{49-8A}+9}{8}$$

$$x=\frac{\sqrt{49-8A}+9}{8}$$

Solve for x

$$x=\frac{-\sqrt{49-8A}+9}{8}$$

$$x=\frac{\sqrt{49-8A}+9}{8}\text{, }A\leq \frac{49}{8}$$