Question 167504This question is from textbook beginning Algebra
: Another solving equations with radicals, please show work, Thank You
square root of x+2 then -2=x
This question is from textbook beginning Algebra
Answer by midwood_trail(310)   (Show Source):
You can put this solution on YOUR website! We have this: sqrt{x + 2} - 2 = x
We want to isolate the square root.
So, add 2 to both sides.
We now have this:
sqrt{x + 2} = x + 2
To remove the square root symbol, square both sides.
Doing so, we get this:
x + 2 = x^2 + 4x + 4
x^2 + 4x - x + 4 - 2 = 0
x^2 + 3x + 2 = 0
Factor this quadratic equation.
(x + 1) (x + 2) = 0
Set each factor to zero and solve for x.
x + 1 = 0
x = -1
=========================
x + 2 = 0
x = -2
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To know for sure that we found the right answers, you must check.
Go back to your original question and replace x with -1 and simplify and then with -2 and simplify again. We want to get the same answer on both sides.
You were given:
sqrt{x + 2} - 2 = x
Let x = -1
sqrt{-1 + 2} - 2 = -1
sqrt{1} - 2 = -1
1 - 2 = -1
-1 = -1...IT CHECKS!!!
So, we know that x = -1.
How about x = -2? Is that true?
Let's check again.
Let x = -2.
sqrt{-2 + 2} - 2 = -2
sqrt{0} - 2 = -2
0 - 2 = -2
-2 = -2...IT ALSO CHECKS!!!
We now know that x = -2 is also a value for x.
Final answer: x = -1 and x = -2
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