Select whether the equation has a solution or not.
[tex]$\sqrt{x}=7$[/tex]
Answer (2)
Square both sides of the equation x = 7 to eliminate the square root.
Simplify the equation to find x = 49 .
Verify the solution by substituting x = 49 back into the original equation: 49 = 7 .
Since the solution is valid, the equation has a solution: roots .
Explanation
Problem Analysis We are given the equation x = 7 and asked to determine if it has a solution.
Isolating x To solve the equation, we need to isolate x . We can do this by squaring both sides of the equation: ( x ) 2 = 7 2
Solving for x Simplifying both sides, we get: x = 49
Checking the Solution Now, we need to check if this solution is valid by substituting x = 49 back into the original equation: 49 = 7
Conclusion Since the square root of 49 is indeed 7, our solution is valid. Therefore, the equation has a solution.
Examples
Consider a scenario where you need to determine the side length of a square garden with an area of 49 square meters. The equation x = 7 models this situation, where x represents the area of the garden and the solution gives the side length. Understanding how to solve such equations allows you to calculate dimensions in various practical applications, such as construction, landscaping, and design.
The equation x = 7 has a solution, which is x = 49 . This is confirmed by substituting x = 49 back into the original equation, resulting in a true statement. Therefore, the equation is valid and has a solution.
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