Solve left(x+1right)^2=x^2+7^2

$${ \left(x+1 \right) }^{ 2 } = { x }^{ 2 } + { 7 }^{ 2 }$$

Solve for x

$$x=24$$

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}.

$$x^{2}+2x+1=x^{2}+7^{2}$$

Calculate 7 to the power of 2 and get 49.

$$x^{2}+2x+1=x^{2}+49$$

Subtract x^{2} from both sides.

$$x^{2}+2x+1-x^{2}=49$$

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

$$2x+1=49$$

Subtract 1 from both sides.

$$2x=49-1$$

Subtract 1 from 49 to get 48.

$$2x=48$$

Divide both sides by 2.

$$x=\frac{48}{2}$$

Divide 48 by 2 to get 24.

$$x=24$$