Solve (3+a)^2=25+16+a^2

$$( 3 + a ) ^ { 2 } = 25 + 16 + a ^ { 2 }$$

Solve for a

$$a = \frac{16}{3} = 5\frac{1}{3} \approx 5.333333333$$

Steps for Solving Linear Equation

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

$$9+6a+a^{2}=25+16+a^{2}$$

Add 25 and 16 to get 41.

$$9+6a+a^{2}=41+a^{2}$$

Subtract a^{2} from both sides.

$$9+6a+a^{2}-a^{2}=41$$

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

$$9+6a=41$$

Subtract 9 from both sides.

$$6a=41-9$$

Subtract 9 from 41 to get 32.

$$6a=32$$

Divide both sides by 6.

$$a=\frac{32}{6}$$

Reduce the fraction \frac{32}{6} to lowest terms by extracting and canceling out 2.

$$a=\frac{16}{3}$$