Select the correct answer.
What is the solution to the equation?
$\sqrt{x}+3=12$
A. 225
B. 81
C. 3
D. no solution
Answer (1)
Isolate the square root term: x = 12 − 3 = 9 .
Square both sides of the equation: x = 9 2 .
Solve for x: x = 81 .
The solution to the equation is 81 .
Explanation
Understanding the Problem We are given the equation x + 3 = 12 and we want to find the value of x that satisfies this equation.
Isolating the Square Root First, we need to isolate the square root term. To do this, we subtract 3 from both sides of the equation: x + 3 − 3 = 12 − 3 x = 9
Squaring Both Sides Now, to get rid of the square root, we square both sides of the equation: ( x ) 2 = 9 2 x = 81
Checking the Solution So, the solution to the equation is x = 81 . Now we need to check our answer by plugging it back into the original equation: 81 + 3 = 9 + 3 = 12 Since this is true, our solution is correct.
Final Answer The solution to the equation x + 3 = 12 is x = 81 . Therefore, the correct answer is B.
Examples
Imagine you're designing a square garden and you know that the length of the fence needed for one side, plus an extra 3 feet for a decorative border, must total 12 feet. This problem helps you calculate the exact length of each side of your garden. By solving the equation x + 3 = 12 , where x is the area of the garden, you determine the side length to be 81 = 9 feet. This ensures your garden fits perfectly within your planned fence length.
