Solve 36+x^2=(x+24)^2

$$36 + x ^ { 2 } = ( x + 24 ) ^ { 2 }$$

Solve for x

$$x = -\frac{45}{4} = -11\frac{1}{4} = -11.25$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+24\right)^{2}.

$$36+x^{2}=x^{2}+48x+576$$

Subtract x^{2} from both sides.

$$36+x^{2}-x^{2}=48x+576$$

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

$$36=48x+576$$

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

$$48x+576=36$$

Subtract 576 from both sides.

$$48x=36-576$$

Subtract 576 from 36 to get -540.

$$48x=-540$$

Divide both sides by 48.

$$x=\frac{-540}{48}$$

Reduce the fraction \frac{-540}{48} to lowest terms by extracting and canceling out 12.

$$x=-\frac{45}{4}$$