Final answer:
The equation x^2 = 50 has two solutions: x = 5√2 and x = -5√2, which can be expressed as x = ±5√2 (option C). This is because the square root of 50 simplifies to 5√2, and both positive and negative values of x will square to 50.
Step-by-step explanation:
To solve for x in the equation x^2 = 50, we need to find the values of x which, when squared, equal 50. This can be done by taking the square root of both sides of the equation:
x^2 = 50
√(x^2) = √(50)
x = ±√(25×2)
x = ±(5√2)
Thus, x equals ±5√2, because the square root of 25 is 5 and the square root of 2 is √2. This means that there are two solutions: x = 5√2 and x = -5√2, which correspond to option C. It's important to include the ± symbol because both 5√2 and -5√2, when squared, will result in 50.