What is the solution of $\sqrt{x+2}-15=-3$?
Answer (2)
To solve x + 2 − 15 = − 3 , first isolate the square root to get x + 2 = 12 , then square both sides to find that x = 142 . Finally, verify the solution to confirm its correctness.
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Isolate the square root: x + 2 = 12 .
Square both sides: x + 2 = 144 .
Solve for x : x = 142 .
Verify the solution: 142 + 2 − 15 = − 3 which simplifies to − 3 = − 3 , confirming the solution. The final answer is 142 .
Explanation
Problem Analysis We are given the equation x + 2 − 15 = − 3 and asked to find the solution for x . We will isolate the square root, square both sides, and solve for x . Finally, we will check our solution to make sure it is valid.
Isolating the Square Root First, we isolate the square root by adding 15 to both sides of the equation: x + 2 − 15 + 15 = − 3 + 15 x + 2 = 12
Eliminating the Square Root Next, we square both sides of the equation to eliminate the square root: ( x + 2 ) 2 = 1 2 2 x + 2 = 144
Solving for x Now, we solve for x by subtracting 2 from both sides of the equation: x + 2 − 2 = 144 − 2 x = 142
Checking the Solution Finally, we check our solution by substituting x = 142 back into the original equation: 142 + 2 − 15 = − 3 144 − 15 = − 3 12 − 15 = − 3 − 3 = − 3 Since the equation holds true, our solution is valid.
Final Answer Therefore, the solution to the equation x + 2 − 15 = − 3 is x = 142 .
Examples
Imagine you are building a square garden and need to determine the length of each side. If the area of the garden plus an additional 2 square feet must equal 144 square feet, you can use the equation x + 2 = 12 to find the side length, x , of the garden. This type of problem arises in various scenarios involving areas, distances, and other geometric relationships.
