Solve (x-2)^2+9^2=(x+1)^2

$$( x - 2 ) ^ { 2 } + 9 ^ { 2 } = ( x + 1 ) ^ { 2 }$$

Solve for x

$$x=14$$

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}.

$$x^{2}-4x+4+9^{2}=\left(x+1\right)^{2}$$

Calculate 9 to the power of 2 and get 81.

$$x^{2}-4x+4+81=\left(x+1\right)^{2}$$

Add 4 and 81 to get 85.

$$x^{2}-4x+85=\left(x+1\right)^{2}$$

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

$$x^{2}-4x+85=x^{2}+2x+1$$

Subtract x^{2} from both sides.

$$x^{2}-4x+85-x^{2}=2x+1$$

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

$$-4x+85=2x+1$$

Subtract 2x from both sides.

$$-4x+85-2x=1$$

Combine -4x and -2x to get -6x.

$$-6x+85=1$$

Subtract 85 from both sides.

$$-6x=1-85$$

Subtract 85 from 1 to get -84.

$$-6x=-84$$

Divide both sides by -6.

$$x=\frac{-84}{-6}$$

Divide -84 by -6 to get 14.

$$x=14$$