Solve a^2+34=(a+4)^2

$$a ^ { 2 } + 34 = ( a + 4 ) ^ { 2 }$$

Solve for a

$$a = \frac{9}{4} = 2\frac{1}{4} = 2.25$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(a+4\right)^{2}.

$$a^{2}+34=a^{2}+8a+16$$

Subtract a^{2} from both sides.

$$a^{2}+34-a^{2}=8a+16$$

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

$$34=8a+16$$

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

$$8a+16=34$$

Subtract 16 from both sides.

$$8a=34-16$$

Subtract 16 from 34 to get 18.

$$8a=18$$

Divide both sides by 8.

$$a=\frac{18}{8}$$

Reduce the fraction \frac{18}{8} to lowest terms by extracting and canceling out 2.

$$a=\frac{9}{4}$$