Solve (x+3)^2=5^2+x^2

$$( x + 3 ) ^ { 2 } = 5 ^ { 2 } + x ^ { 2 }$$

Solve for x

$$x = \frac{8}{3} = 2\frac{2}{3} \approx 2.666666667$$

Steps for Solving Linear Equation

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

$$x^{2}+6x+9=5^{2}+x^{2}$$

Calculate 5 to the power of 2 and get 25.

$$x^{2}+6x+9=25+x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}+6x+9-x^{2}=25$$

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

$$6x+9=25$$

Subtract 9 from both sides.

$$6x=25-9$$

Subtract 9 from 25 to get 16.

$$6x=16$$

Divide both sides by 6.

$$x=\frac{16}{6}$$

Reduce the fraction \frac{16}{6} to lowest terms by extracting and canceling out 2.

$$x=\frac{8}{3}$$