Which choice correctly shows the solution(s) of the equation x2 = 400?
The Correct Answer and Explanation is:
To solve the equation (x^2 = 400), we need to find the values of (x) that satisfy this equation.
Step 1: Isolate (x^2)
The equation is already in the form (x^2 = 400).
Step 2: Take the square root of both sides
To find (x), we take the square root of both sides. However, when taking the square root in algebra, it is essential to consider both the positive and negative roots:
[
x = \sqrt{400} \quad \text{and} \quad x = -\sqrt{400}
]
Step 3: Calculate the square root
Calculating the square root of 400 gives:
[
\sqrt{400} = 20
]
Step 4: Write the solutions
Thus, the solutions to the equation are:
[
x = 20 \quad \text{and} \quad x = -20
]
Conclusion
The complete solution set can be expressed as (x = \pm 20). This means there are two solutions: (x = 20) and (x = -20). Both values satisfy the original equation when substituted back into (x^2 = 400):
- For (x = 20):
[
20^2 = 400
]
- For (x = -20):
[
(-20)^2 = 400
]
Summary
The equation (x^2 = 400) has two solutions: (x = 20) and (x = -20). This reflects the property of quadratic equations, which often yield two solutions due to the nature of squaring a number, where both a positive and a negative value can produce the same result when squared. Thus, the correct answer indicating the solutions is (x = 20) and (x = -20).