Solve 20+left(x-1right)^2+left(x-3right)^2=left(x+1right)^2+left(x+1right)^2

$$20+ { \left(x-1 \right) }^{ 2 } + { \left(x-3 \right) }^{ 2 } = { \left(x+1 \right) }^{ 2 } + { \left(x+1 \right) }^{ 2 }$$

Solve for x

$$x = \frac{7}{3} = 2\frac{1}{3} \approx 2.333333333$$

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}.

$$20+x^{2}-2x+1+\left(x-3\right)^{2}=\left(x+1\right)^{2}+\left(x+1\right)^{2}$$

Add 20 and 1 to get 21.

$$21+x^{2}-2x+\left(x-3\right)^{2}=\left(x+1\right)^{2}+\left(x+1\right)^{2}$$

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

$$21+x^{2}-2x+x^{2}-6x+9=\left(x+1\right)^{2}+\left(x+1\right)^{2}$$

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

$$21+2x^{2}-2x-6x+9=\left(x+1\right)^{2}+\left(x+1\right)^{2}$$

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

$$21+2x^{2}-8x+9=\left(x+1\right)^{2}+\left(x+1\right)^{2}$$

Add 21 and 9 to get 30.

$$30+2x^{2}-8x=\left(x+1\right)^{2}+\left(x+1\right)^{2}$$

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

$$30+2x^{2}-8x=x^{2}+2x+1+\left(x+1\right)^{2}$$

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

$$30+2x^{2}-8x=x^{2}+2x+1+x^{2}+2x+1$$

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

$$30+2x^{2}-8x=2x^{2}+2x+1+2x+1$$

Combine 2x and 2x to get 4x.

$$30+2x^{2}-8x=2x^{2}+4x+1+1$$

Add 1 and 1 to get 2.

$$30+2x^{2}-8x=2x^{2}+4x+2$$

Subtract 2x^{2} from both sides.

$$30+2x^{2}-8x-2x^{2}=4x+2$$

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

$$30-8x=4x+2$$

Subtract 4x from both sides.

$$30-8x-4x=2$$

Combine -8x and -4x to get -12x.

$$30-12x=2$$

Subtract 30 from both sides.

$$-12x=2-30$$

Subtract 30 from 2 to get -28.

$$-12x=-28$$

Divide both sides by -12.

$$x=\frac{-28}{-12}$$

Reduce the fraction \frac{-28}{-12} to lowest terms by extracting and canceling out -4.

$$x=\frac{7}{3}$$