Solve (x-1)^2=(x+3)^2

$$( x - 1 ) ^ { 2 } = ( x + 3 ) ^ { 2 }$$

Solve for x

$$x=-1$$

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}.

$$x^{2}-2x+1=\left(x+3\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+3\right)^{2}.

$$x^{2}-2x+1=x^{2}+6x+9$$

Subtract x^{2} from both sides.

$$x^{2}-2x+1-x^{2}=6x+9$$

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

$$-2x+1=6x+9$$

Subtract 6x from both sides.

$$-2x+1-6x=9$$

Combine -2x and -6x to get -8x.

$$-8x+1=9$$

Subtract 1 from both sides.

$$-8x=9-1$$

Subtract 1 from 9 to get 8.

$$-8x=8$$

Divide both sides by -8.

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

Divide 8 by -8 to get -1.

$$x=-1$$