Video Explanation

Text Explanation

First we need to get rid of the square root. To do that, square both sides:

(x – 5)² = 

FOIL the left side and remove the radical on the right:

x²  − 10x + 25 = 2x² −18x + 37

Next combine like terms.

0 = x² − 8x + 12

Factor:

0=(x − 2)(x − 6)

x = 2, 6

Don't forget that when we square a square root, we might have introduced a false solution. It's important to plug both 2 and 6 back in to see if we get a contradiction. When we plug in 2, we find a problem:

2 − 5 = 

−3 = 

−3 = 3

This is a contradiction, so x = 2 isn't really an answer. That's why the answer is x = 6.

Frequently Asked Questions

FAQ: The two solutions are x = 2 and x = 6. However, only 6 was selected as the answer based on the assumption that –3 is not equal to . However,  can be either 3 or −3 so why is this not a viable answer?

A:  The radical sign (more commonly known as the square root sign) actually means the POSITIVE square root of a given number. This positive square root is often referred to as the principal square root. Anytime we see the radical sign on the GRE, we want the principal (positive) square root.

We cover this concept in our lesson video on square roots here:

• GRE - Square Roots
• GMAT - Square Roots

So this is why we can ignore x = 2. When it gives us an answer of (−3) = , we know that's not possible based on the above definition of the square root or radical sign that the square root must be a positive number :D