Solve left(x+2right)^2=32+left(x-2right)^2

$${ \left(x+2 \right) }^{ 2 } =32+ { \left(x-2 \right) }^{ 2 }$$

Solve for x

$$x=4$$

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}.

$$x^{2}+4x+4=32+\left(x-2\right)^{2}$$

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

$$x^{2}+4x+4=32+x^{2}-4x+4$$

Add 32 and 4 to get 36.

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

Subtract x^{2} from both sides.

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

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

$$4x+4=36-4x$$

Add 4x to both sides.

$$4x+4+4x=36$$

Combine 4x and 4x to get 8x.

$$8x+4=36$$

Subtract 4 from both sides.

$$8x=36-4$$

Subtract 4 from 36 to get 32.

$$8x=32$$

Divide both sides by 8.

$$x=\frac{32}{8}$$

Divide 32 by 8 to get 4.

$$x=4$$