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

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

Solve for a (complex solution)

$$\left\{\begin{matrix}\\a=4\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

Swap sides so that all variable terms are on the left hand side.

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

Subtract x^{2} from both sides.

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

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

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

Subtract 4 from both sides.

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

Subtract 4 from 4 to get 0.

$$ax=4x$$

The equation is in standard form.

$$xa=4x$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{4x}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{4x}{x}$$

Divide 4x by x.

$$a=4$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&a=4\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

Subtract x^{2} from both sides.

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

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

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

Subtract ax from both sides.

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

Subtract 4 from both sides.

$$4x-ax=4-4$$

Subtract 4 from 4 to get 0.

$$4x-ax=0$$

Combine all terms containing x.

$$\left(4-a\right)x=0$$

Divide 0 by 4-a.

$$x=0$$

Solve for a

$$\left\{\begin{matrix}\\a=4\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

Swap sides so that all variable terms are on the left hand side.

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

Subtract x^{2} from both sides.

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

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

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

Subtract 4 from both sides.

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

Subtract 4 from 4 to get 0.

$$ax=4x$$

The equation is in standard form.

$$xa=4x$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{4x}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{4x}{x}$$

Divide 4x by x.

$$a=4$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&a=4\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

Subtract x^{2} from both sides.

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

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

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

Subtract ax from both sides.

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

Subtract 4 from both sides.

$$4x-ax=4-4$$

Subtract 4 from 4 to get 0.

$$4x-ax=0$$

Combine all terms containing x.

$$\left(4-a\right)x=0$$

Divide 0 by 4-a.

$$x=0$$