Solve x^2=(7.2+x)^2-18.7^2

$$x ^ { 2 } = ( 7.2 + x ) ^ { 2 } - 18.7 ^ { 2 }$$

Solve for x

$$x = \frac{5957}{288} = 20\frac{197}{288} \approx 20.684027778$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(7.2+x\right)^{2}.

$$x^{2}=51.84+14.4x+x^{2}-18.7^{2}$$

Calculate 18.7 to the power of 2 and get 349.69.

$$x^{2}=51.84+14.4x+x^{2}-349.69$$

Subtract 349.69 from 51.84 to get -297.85.

$$x^{2}=-297.85+14.4x+x^{2}$$

Subtract 14.4x from both sides.

$$x^{2}-14.4x=-297.85+x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}-14.4x-x^{2}=-297.85$$

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

$$-14.4x=-297.85$$

Divide both sides by -14.4.

$$x=\frac{-297.85}{-14.4}$$

Expand \frac{-297.85}{-14.4} by multiplying both numerator and the denominator by 100.

$$x=\frac{-29785}{-1440}$$

Reduce the fraction \frac{-29785}{-1440} to lowest terms by extracting and canceling out -5.

$$x=\frac{5957}{288}$$