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

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

Solve for A

$$A=2\left(3-2x\right)\left(x+2\right)$$

Solution Steps

Use the distributive property to multiply -2 by x^{2}-4.

$$A=x^{2}+4x+4-3x\left(x+2\right)-2x^{2}+8$$

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

$$A=x^{2}+4x+4-3x^{2}-6x-2x^{2}+8$$

Combine x^{2} and -3x^{2} to get -2x^{2}.

$$A=-2x^{2}+4x+4-6x-2x^{2}+8$$

Combine 4x and -6x to get -2x.

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

Combine -2x^{2} and -2x^{2} to get -4x^{2}.

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

Add 4 and 8 to get 12.

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

Solve for x (complex solution)

$$x=\frac{-\sqrt{49-4A}-1}{4}$$

$$x=\frac{\sqrt{49-4A}-1}{4}$$

Solve for x

$$x=\frac{-\sqrt{49-4A}-1}{4}$$

$$x=\frac{\sqrt{49-4A}-1}{4}\text{, }A\leq \frac{49}{4}$$