If something² = 225, then EITHER something = 15 OR something = -15

GIVEN: (x + 3)² = 225
This means EITHER (x + 3) = 15 OR (x + 3) = -15

Let's examine both cases:

Case a: (x + 3) = 15
Subtract 4 from both sides to get: x - 1 = 11
Check the answer choices . . . not there.

Case b: (x + 3) = -15
Subtract 4 from both sides to get: x - 1 = -19
Check the answer choices . . . BINGO!

Answer: E

Cheers,
Brent

I tried a different approach:

If A) x-1=13 > x=14

Then,

B) x=13
C) x=-11
D) x=-15
E) x=-18

As (x+3)^2=225, I need to pick one option equal to 225
A) (14+3)^2= 225
B) (13+3)^2 =225
C) (-11+3)^2= 225
D) (-15+3)^2= 225
E) (-18+3)^2= 225

So the answer is E

I'm wondering why this one has so few correct answers. A lot of the time on the GRE quant I start to think diagnosing why so many get something wrong is better than diagnosing how they got it right.

Guessing most just root each side, see their answer of 11 doesn't exist, and guess. Key here is that when you take the root of a variable you have to set whatever was rooted to an absolute value. The absolute value must be considered as both possibly being positive and possibly being negative. Solve for each.

If 15-3=12
Then x-1 = 12-1=-11 is the right ans which is not visible in ans choices.

Posted from my mobile device

Thanks for the good explanations all. If I could summarize in my own words:

Step 1: Take the square root of each side. (x+3)^2 = 225. This turns into x+3 = 15 because 15 is the square root of 225.
Step 2: We have two answers here because a square could have a negative and positive root (15^2 = 225, -15^2 = 225). x+3 = 15 OR x+3 = -15
Step 3: The first answer could be x = 15-3 = 12. 12-1 = 11. That is not in the answer choices so we can eliminate that answer.
Step 4: The second answer could be x = -15-3 = -18. -18-1 = -19. That is in the answer choices so the correct answer is E, 19.

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This is how I solved it... GIVEN: (x + 3)² = 225. expanded using foil to get x² + 6x + 9 = 225. -225 from both sides to get x² + 6x + 9 - 225 = 225 - 225 = x² + 6x + 216 = 0. Which can be factorized to get (x + 18) (x - 12) = 0. So x = -18, x = 12. But only one solution of x is defined and that is x = -18. If we plug -18 into x² + 6x + 9 = 225, we'll get 225 = 225. Thus x-1 when x = -18 = (-18) - 1 = -19. therefore E is the answer. Hope this helps!