Solve (x+2)(x+2)=x^2+4x+4

$$( x + 2 ) ( x + 2 ) = x ^ { 2 } + 4 x + 4$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

Solution Steps

Multiply x+2 and x+2 to get \left(x+2\right)^{2}.

$$\left(x+2\right)^{2}=x^{2}+4x+4$$

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

$$x^{2}+4x+4=x^{2}+4x+4$$

Subtract x^{2} from both sides.

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

Combine x^{2} and -x^{2} to get 0.

$$4x+4=4x+4$$

Subtract 4x from both sides.

$$4x+4-4x=4$$

Combine 4x and -4x to get 0.

$$4=4$$

Compare 4 and 4.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{C}$$

Solve for x

$$x\in \mathrm{R}$$

Solution Steps

Multiply x+2 and x+2 to get \left(x+2\right)^{2}.

$$\left(x+2\right)^{2}=x^{2}+4x+4$$

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

$$x^{2}+4x+4=x^{2}+4x+4$$

Subtract x^{2} from both sides.

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

Combine x^{2} and -x^{2} to get 0.

$$4x+4=4x+4$$

Subtract 4x from both sides.

$$4x+4-4x=4$$

Combine 4x and -4x to get 0.

$$4=4$$

Compare 4 and 4.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$