How do you solve ${x^2} = 64$$?$

Hint: First of all, find the common factor of the given quadratic equation in the question. After finding the common factor apply zero product property and set each variable factor equal to zero.

Complete step by step solution:
We have been given that we have to find the value of x, ${x^2} = 64$. So first we will move all the terms to one side of the equation, usually the left, using the addition and subtraction property.
Then factoring the given quadratic equation according to the given expression and then apply the zero product property and set each variable factor equal to zero. So, the given quadratic equation is,
$ \Rightarrow {x^2} = 64$
From the above expression, we have to move the all the terms to one side of the equation usually the left side,
$ \Rightarrow {x^2} - 64 = 0$
After moving all the terms of the equation we get –
$ \Rightarrow {x^2} - 64 = 0$
 Doing further operations to solve the quadratic polynomial that we usually do,
$ \Rightarrow {x^2} + 8x - 8x + 64 = 0$
Then take the common from this equation, we get –
$ \Rightarrow x\left( {x + 8} \right) - 8\left( {x + 8} \right) = 0$
Now, we have two factors (x+8) and (x-8).
 $ \Rightarrow \left( {x + 8} \right)\left( {x - 8} \right) = 0$
Then, we will set each factor equal to zero and we get –
Two subproblems:
$ \Rightarrow \left( {x + 8} \right) = 0$
$ \Rightarrow $$\left( {x - 8} \right) = 0$
Solving the first subproblems, we get –
$ \Rightarrow $$\left( {x + 8} \right) = 0$, gives $x = - 8$
Again, solving the second subproblems, we get –
$ \Rightarrow $$\left( {x - 8} \right) = 0$, gives $x = 8$
                 Or
$ \Rightarrow $$x = \pm 8$

Hence, the required answer is, $ \pm 8$

Note:
We can also solve this question by the alternative method: Taking the square root of both sides of this equation. When we do the square root of any number, we get two values one the positive and another negative value.