Final Answer:
The solution to the equation x^(2) - 28 = 0 is x = ±√28 or x = ±2√7 in simplest radical form.
Step-by-step explanation:
To find the solution to the equation x^(2) - 28 = 0, we can start by adding 28 to both sides to isolate the x^(2) term. This gives us x^(2) = 28. To solve for x, we take the square root of both sides, resulting in x = ±√28. Now, we simplify the radical expression by factoring 28 into its prime factors: 28 = 2 * 2 * 7. Taking the square root of this expression, we get x = ±√(2^2 * 7) = ±(2√7). Therefore, the solution in simplest radical form is x = ±2√7.
In the given equation, x can be either positive or negative since squaring any real number yields a positive result. The ± symbol accounts for both possibilities. The expression 2√7 represents the simplified radical form, as it incorporates the prime factorization of 28. Thus, the final answer to x^(2) - 28 = 0 is x = ±2√7. This solution captures all possible values of x that satisfy the original equation.