Solve x^2+8=(x+1)^2-23

$$x ^ { 2 } + 8 = ( x + 1 ) ^ { 2 } - 23$$

Solve for x

$$x=15$$

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}.

$$x^{2}+8=x^{2}+2x+1-23$$

Subtract 23 from 1 to get -22.

$$x^{2}+8=x^{2}+2x-22$$

Subtract x^{2} from both sides.

$$x^{2}+8-x^{2}=2x-22$$

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

$$8=2x-22$$

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

$$2x-22=8$$

Add 22 to both sides.

$$2x=8+22$$

Add 8 and 22 to get 30.

$$2x=30$$

Divide both sides by 2.

$$x=\frac{30}{2}$$

Divide 30 by 2 to get 15.

$$x=15$$