Solve y=f(x)=4*2(2x+1)-(2x+6)^2

$$y = f ( x ) = 4 \cdot 2 ( 2 x + 1 ) - ( 2 x + 6 ) ^ { 2 }$$

Solve for y

$$y=-4x^{2}-8x-28$$

Solution Steps

Multiply 4 and 2 to get 8.

$$y=8\left(2x+1\right)-\left(2x+6\right)^{2}$$

Use the distributive property to multiply 8 by 2x+1.

$$y=16x+8-\left(2x+6\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+6\right)^{2}.

$$y=16x+8-\left(4x^{2}+24x+36\right)$$

To find the opposite of 4x^{2}+24x+36, find the opposite of each term.

$$y=16x+8-4x^{2}-24x-36$$

Combine 16x and -24x to get -8x.

$$y=-8x+8-4x^{2}-36$$

Subtract 36 from 8 to get -28.

$$y=-8x-28-4x^{2}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{-y-24}}{2}-1$$

$$x=-\frac{\sqrt{-y-24}}{2}-1$$

Solve for x

$$x=-\frac{\sqrt{-y-24}}{2}-1$$

$$x=\frac{\sqrt{-y-24}}{2}-1\text{, }y\leq -24$$