Question 640197: Solve for X: √(X+5)=X-1
(√(X+5))^2=(X-1)^2
X+5=X^2-2X+1
X^2-3X-4=0
Answer by josh_jordan(263)   (Show Source):
You can put this solution on YOUR website! Almost there! :) Last line says: 
We can solve for x in 3 different ways: factoring, completing the square, or using the quadratic formula. The easiest of these ways is factoring, so let's see if we can factor this equation.
Let's look at the number at the end of the left side of the equal sign: -4
Now let's look at the middle number/variable: -3.
For us to be able to solve by factoring, we need to have 2 numbers that multiply together to equal -4 AND can be added together to equal -3. Let's look at the products of -4:
-1 x 4 = -4
1 x -4 = -4
2 x -2 = -4
-2 x 2 = -4
Now, let's add each of these products to see if they equal -3:
-1 + 4 = 3
1 + -4 = -3
We can stop right there, because 1 + -4 = -3
So, can be re-written as
 = 
AND
 = 
To find out if both of these numbers are solutions, we will substitute x in our original equation for each of our possible solutions:
 =  =
 =
Since 2 does NOT equal -2, we know that -1 is NOT a solution
Now let's try 4:
=  =
 =
Since both sides of the equal sign are the same, 4 IS a solution.
FINAL ANSWER: x = 4
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