Solve (y+6)^2 - 8 = 0, where y is a real number.

Question

Simplify the answer as much as possible.

Answer 1

Good Morning!

So, here is what I did...

Let's start with the original of (y + 6)² - 8 = 0

Since this is a straightforward quadratic, we can just solve using inverse operations and not worry about expanding the (y+6)², simplifying and factoring. Plus, once we simplify, we may end up with a trinomial that's not factorable anyways..

Here we go...

Step 1) add 8 to both sides to yield (y+6)² = 8

Step 2) square root both sides being mindful that when you take the square root of a number, most times you have to take into account BOTH positive and negative values... this then yields y+6 = ±√8

Step 3) subtract 6 on both sides to yield y = -6 ±√8

Step 4) since this question asks us to simplify "as much as possible," we have to simplify ±√8 to ±2√2... If you want clarification on how this is done, please reply and I will walk you through it...

Step 5) box up our final solution of y = -6 ±2√2

Let me know if this helps!! :)

Answer 2

(y+6)² - 8 = 0

(y+6)² = 8

y + 6 = ±√8

y = -6 ± √8

y = -3.172, -8.828