Solve x^2+62=(x+1)^2-37

$$x ^ { 2 } + 62 = ( x + 1 ) ^ { 2 } - 37$$

Solve for x

$$x=49$$

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}.

$$x^{2}+62=x^{2}+2x+1-37$$

Subtract 37 from 1 to get -36.

$$x^{2}+62=x^{2}+2x-36$$

Subtract x^{2} from both sides.

$$x^{2}+62-x^{2}=2x-36$$

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

$$62=2x-36$$

Swap sides so that all variable terms are on the left hand side.

$$2x-36=62$$

Add 36 to both sides.

$$2x=62+36$$

Add 62 and 36 to get 98.

$$2x=98$$

Divide both sides by 2.

$$x=\frac{98}{2}$$

Divide 98 by 2 to get 49.

$$x=49$$