Lesson: Basic Equation Solving

Comment on Basic Equation Solving

Hey Brent can you help me factor this out 9x^2+6x+1=0? Icant seem to comprehend the steps
greenlight-admin's picture

If the quadratic is NOT in the form x² + bx + c = 0, then it is very likely going to be in the form of one of the 2 SPECIAL PRODUCTS:

(x + y)² = x² + 2xy + y²
(x - y)² = x² - 2xy + y²

Here are some examples of Special Products:
4x² + 4x + 1 = (2x + 1)²
25x² - 10x + 1 = (5x - 1)²
9x² + 42x + 49 = (3x + 7)²

Notice the pattern?
In the 1st example, 4x² = (2x)(2x), 1 = (1)(1), and 4x = (2)(2x)(1)
In the 2nd example, 25x² = (5x)(5x), 1 = (1)(1), and 10x = (2)(5x)(7)
In the 3rd example, 9x² = (3x)(3x), 49 = (7)(7), and 42x = (2)(3x)(7)

Notice that 9x² + 6x + 1 = 0 is also a special product.
9x² = (3x)(3x), 1 = (1)(1), and 6x = (2)(3x)(1)

So, we can factor to get: (3x + 1)² = 0
This means 3x + 1 = 0
So, 3x = -1
x = -1/3

For more on Special Products, watch https://www.greenlighttestprep.com/module/gre-algebra-and-equation-solvi... (start video at 4:48)


Hi Brent ,
for https://greprepclub.com/forum/the-integers-x-and-y-are-greater-than-1-if-4x-7y-2148.html

I had approached in this way
and from there 2*2=4 and multipled with 3
i.e considereed 3 as x
7*9 - considered y as 9

I got the answer but is this a correct approach to follow

greenlight-admin's picture

Question link: https://greprepclub.com/forum/the-integers-x-and-y-are-greater-than-1-if...

Yes, that approach works perfectly.


can you explain to me the one that says quant a= n^2. I solved with two different sets of numbers, one gave me equal and one gave me not equal
greenlight-admin's picture

Can you please provide a link to the question. Otherwise it'll take me a long time to find the question you're referring to.

It is the second question under difficulty level 150-159
greenlight-admin's picture

Question link: https://greprepclub.com/forum/n-2k-3m-15913.html
Please tell me the values you used that caused the two quantities to be not equal, and I'll take a look.

I apologize, I wrote the 3 as a 2 by mistake.
greenlight-admin's picture

No problem. It happens to me all the time :-)

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