#### Answer

a. The logical first step in solving $(x-5)^{2} = 64$ would be to take the square root of both sides.
b. The logical first step in solving $(x+5)^{2}+5=64$ is to take subtract 5 from both sides.
c. The logical first step in solving $x^{2} + x =2$ is to subtract 2 from both sides.

#### Work Step by Step

a. $(x-5)^{2}$ can be solved using the square root method, as $\sqrt (x-5)^{2} = x-5$ and $\sqrt 64 = 8$. After taking the square root of both sides, the equation is reduced to:$(x-5)=8$.
b. $(x+5)^{2} + 5 = 64$ can be also be solved using the square root method, after the binomial is on one side and the number is on the other:$(x+5)^{2} = 59$ The next logical step would be to take the square root of each side and reduce the equation to: $(x+5)^{2} = \sqrt 59$
c. $x^{2} +x = 2$ can be solved using the quadratic formula after 2 is taken from both sides and the equation is simplified to $x^2 + x -2 = 0$