Solve 16+1+(a-7)^2=3^2+5^2+(a+2)^2

$$16 + 1 + ( a - 7 ) ^ { 2 } = 3 ^ { 2 } + 5 ^ { 2 } + ( a + 2 ) ^ { 2 }$$

Solve for a

$$a = \frac{14}{9} = 1\frac{5}{9} \approx 1.555555556$$

Steps for Solving Linear Equation

Add 16 and 1 to get 17.

$$17+\left(a-7\right)^{2}=3^{2}+5^{2}+\left(a+2\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(a-7\right)^{2}.

$$17+a^{2}-14a+49=3^{2}+5^{2}+\left(a+2\right)^{2}$$

Add 17 and 49 to get 66.

$$66+a^{2}-14a=3^{2}+5^{2}+\left(a+2\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$66+a^{2}-14a=9+5^{2}+\left(a+2\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$66+a^{2}-14a=9+25+\left(a+2\right)^{2}$$

Add 9 and 25 to get 34.

$$66+a^{2}-14a=34+\left(a+2\right)^{2}$$

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

$$66+a^{2}-14a=34+a^{2}+4a+4$$

Add 34 and 4 to get 38.

$$66+a^{2}-14a=38+a^{2}+4a$$

Subtract a^{2} from both sides.

$$66+a^{2}-14a-a^{2}=38+4a$$

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

$$66-14a=38+4a$$

Subtract 4a from both sides.

$$66-14a-4a=38$$

Combine -14a and -4a to get -18a.

$$66-18a=38$$

Subtract 66 from both sides.

$$-18a=38-66$$

Subtract 66 from 38 to get -28.

$$-18a=-28$$

Divide both sides by -18.

$$a=\frac{-28}{-18}$$

Reduce the fraction \frac{-28}{-18} to lowest terms by extracting and canceling out -2.

$$a=\frac{14}{9}$$