Question: x/2 and so on

Comment on x/2 and so on

Hey Brent!
This is a good example of when your idea of "something" comes handy.
As soon as I got x^2 + 4x + 2 = 0, I simply said "something + 2 = 0, which means "something" + 5 has to = 3.
gmat-admin's picture

Awesome solution - well done!

For others reading this, here's the video on the Something Method:

Hi Brent,

Could you explain how we can use the something method here. I've seen the video related to this topic but still a bit rusty.

gmat-admin's picture

When we cross multiply the original equation, we get: x² + 10x = 6x - 2
Rearrange to get: x² + 4x + 2 = 0

Our goal is to find the value of x² + 4x + 5
abrahamic01 thought of this as something + 5

abrahamic01 noted that we can think of x² + 4x + 2 = 0 as something + 2 = 0

So, to get "something + 5", we need to take the equation "something + 2 = 0" and add 3 to both sides to get: "something + 5 = 3"
In other words, " x² + 4x + 5 = 3"

For this question, I cross multiplied the given, then factored to get solutions of x=-2 or x=-6

Then, plugging in these two potential solutions showed me that x=-2 yielded one of the answer choices, so that answer choice ( B) must be the solution.

Where did I go wrong?
gmat-admin's picture

Without seeing your steps, it's hard to tell what happened.

In the video solution, I also cross multiplied the given equation.
When I did so, I got the equation: x² + 4x + 2 = 0

The left side of this equation cannot be factored, so I'm not sure how you got the solutions x = -2 and x = -6

That said, your strategy is correct; you just made an error at some point after you cross multiplied.

Hi Brent, I have a question for you.
If we have x² + 4X + 2, it means that we have (x+2)². So x=-2.
If we substitute x = -2 to x² + 4X + 5, we have --> 4 - 8 + 5 --> = 1.
So, I understood the other method but I first tried this one, and in this case, the solution should be B. Can you help me?
gmat-admin's picture

There are a few problems with your solution.
To begin, x² + 4x + 2 doesn't factor to equal (x + 2)²
Instead, x² + 4x + 4 = (x + 2)²

Also, x² + 4x + 2 isn't an equation; it's an expression that has infinitely many values, depending on the value of x.
Since x² + 4x + 2 isn't that equation, it can't be solved.
So, even if the question provided the expression x² + 4x + 4, there's still no way to solve it, because it's not an equation.

On the other hand, if we have the equation x² + 4x + 4 = 0, then we can factor the left side to get: (x + 2)(x + 2) = 0, in which case the solution is x = -2

Does that help?

Hello Brent, you are totally right. Sometimes it's better to take a rest and refresh the mind instead of making such errors! Thanks again!

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