Solve left(3+xright)^2-40^2=x^2

$${ \left(3+x \right) }^{ 2 } - { 40 }^{ 2 } = { x }^{ 2 }$$

Solve for x

$$x = \frac{1591}{6} = 265\frac{1}{6} \approx 265.166666667$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3+x\right)^{2}.

$$9+6x+x^{2}-40^{2}=x^{2}$$

Calculate 40 to the power of 2 and get 1600.

$$9+6x+x^{2}-1600=x^{2}$$

Subtract 1600 from 9 to get -1591.

$$-1591+6x+x^{2}=x^{2}$$

Subtract x^{2} from both sides.

$$-1591+6x+x^{2}-x^{2}=0$$

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

$$-1591+6x=0$$

Add 1591 to both sides. Anything plus zero gives itself.

$$6x=1591$$

Divide both sides by 6.

$$x=\frac{1591}{6}$$