Solve x^2=left(x+30right)^2-60^2

$${ x }^{ 2 } = { \left(x+30 \right) }^{ 2 } - { 60 }^{ 2 }$$

Solve for x

$$x=45$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+30\right)^{2}.

$$x^{2}=x^{2}+60x+900-60^{2}$$

Calculate 60 to the power of 2 and get 3600.

$$x^{2}=x^{2}+60x+900-3600$$

Subtract 3600 from 900 to get -2700.

$$x^{2}=x^{2}+60x-2700$$

Subtract x^{2} from both sides.

$$x^{2}-x^{2}=60x-2700$$

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

$$0=60x-2700$$

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

$$60x-2700=0$$

Add 2700 to both sides. Anything plus zero gives itself.

$$60x=2700$$

Divide both sides by 60.

$$x=\frac{2700}{60}$$

Divide 2700 by 60 to get 45.

$$x=45$$