Solve x^2+15=(x+1)^2-26

$$x ^ { 2 } + 15 = ( x + 1 ) ^ { 2 } - 26$$

Solve for x

$$x=20$$

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}.

$$x^{2}+15=x^{2}+2x+1-26$$

Subtract 26 from 1 to get -25.

$$x^{2}+15=x^{2}+2x-25$$

Subtract x^{2} from both sides.

$$x^{2}+15-x^{2}=2x-25$$

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

$$15=2x-25$$

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

$$2x-25=15$$

Add 25 to both sides.

$$2x=15+25$$

Add 15 and 25 to get 40.

$$2x=40$$

Divide both sides by 2.

$$x=\frac{40}{2}$$

Divide 40 by 2 to get 20.

$$x=20$$