√(x+2) -7 =√(x+9)
If you could show your work on how to get the answer that would be awesome. I really need to learn how to do this
To solve this equation, we need to isolate the variable on one side of the equation. Let's go step by step:
1. Start by squaring both sides of the equation to eliminate the square roots:
(√(x+2) - 7)² = (√(x+9))²
2. Simplify both sides:
(x+2) - 14(√(x+2)) + 49 = x + 9
3. Collect like terms on each side:
x + 2 - x - 9 = 14(√(x+2)) - 49
4. Simplify further:
-7 = 14(√(x+2)) - 49
5. Move the terms without square roots to one side and the terms with square roots to the other side:
14(√(x+2)) = 49 - 7
6. Simplify:
14(√(x+2)) = 42
7. Divide both sides of the equation by 14 to isolate the square root:
√(x+2) = 3
8. Square both sides to eliminate the square root:
(√(x+2))² = 3²
9. Simplify:
x + 2 = 9
10. Finally, solve for x by subtracting 2 from both sides:
x = 9 - 2
11. The solution is x = 7.
So, the solution to the equation √(x+2) - 7 = √(x+9) is x = 7.