Solve (x+6)^2-2=(x-5)^2+2

$$( x + 6 ) ^ { 2 } - 2 = ( x - 5 ) ^ { 2 } + 2$$

Solve for x

$$x=-\frac{7}{22}\approx -0.318181818$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+6\right)^{2}.

$$x^{2}+12x+36-2=\left(x-5\right)^{2}+2$$

Subtract 2 from 36 to get 34.

$$x^{2}+12x+34=\left(x-5\right)^{2}+2$$

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

$$x^{2}+12x+34=x^{2}-10x+25+2$$

Add 25 and 2 to get 27.

$$x^{2}+12x+34=x^{2}-10x+27$$

Subtract x^{2} from both sides.

$$x^{2}+12x+34-x^{2}=-10x+27$$

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

$$12x+34=-10x+27$$

Add 10x to both sides.

$$12x+34+10x=27$$

Combine 12x and 10x to get 22x.

$$22x+34=27$$

Subtract 34 from both sides.

$$22x=27-34$$

Subtract 34 from 27 to get -7.

$$22x=-7$$

Divide both sides by 22.

$$x=\frac{-7}{22}$$

Fraction \frac{-7}{22} can be rewritten as -\frac{7}{22} by extracting the negative sign.

$$x=-\frac{7}{22}$$