Solve left(x+1right)^2=left(x-5right)^2

$${ \left(x+1 \right) }^{ 2 } = { \left(x-5 \right) }^{ 2 }$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

$$x^{2}+2x+1=\left(x-5\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-5\right)^{2}.

$$x^{2}+2x+1=x^{2}-10x+25$$

Subtract x^{2} from both sides.

$$x^{2}+2x+1-x^{2}=-10x+25$$

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

$$2x+1=-10x+25$$

Add 10x to both sides.

$$2x+1+10x=25$$

Combine 2x and 10x to get 12x.

$$12x+1=25$$

Subtract 1 from both sides.

$$12x=25-1$$

Subtract 1 from 25 to get 24.

$$12x=24$$

Divide both sides by 12.

$$x=\frac{24}{12}$$

Divide 24 by 12 to get 2.

$$x=2$$