If (2y - 5)^2 = 361, which of the following could be the value of y+2

Answer = E = -5

\((2y - 5)^2 = 361\)

2y - 5 = +/- 19

2y = 5+19 = 24 OR 5-19 = -14

y = 12 OR y = -7

y+2 = 14 OR y+2 = -5

Answer = E

By solving and reducing the equation we get 'Y^2 - 5 Y -84 = 0'

so (Y-12) (Y+7) = 0 -> Y = 12 ; Y = -7

Therefore Y+2 is 14 or -5. Only -5 is given in the options.

Hence Answer 'E'

(2y - 5)^2 = 361 ---> 2y - 5 = 19, 2y - 5 = -19

By solving above 2 equations we will get y = 12, -7

Now y + 2 = 14,-5

From the given options E --> -5 is the answer.

Official Solution:

If \((2y - 5)^2 = 361\), which of the following could be the value of \(y + 2\)?

A. 24
B. 19
C. 12
D. -7
E. -5

The question asks for the value of \(y + 2\), given an equation for \(y\).

The first step is to solve for \(y\) in the given equation. Since the right side of this equation is a perfect square, it will be fastest to take the square root of both sides.

Doing so, we find: \((2y - 5) = \pm 19\). Note that the square root can be positive or negative.

We rewrite this equation as two equations, one for each root: \(2y - 5 = -19\) or \(2y - 5 = 19\).

We solve for \(y\) in one equation: \(2y = -14\), \(y = -7\).

We solve for \(y\) in the other equation: \(2y = 24\), \(y = 12\).

Now we can solve for \(y + 2\). Adding 2 to each of our solutions, we find that either \(y + 2 = -5\) or \(y + 2 = 14\).

Answer: E.

How I approached this question was taking a look at both sides. If you move all the terms on one side you notice a difference of squares
\(a^2-b^2\)

\(361 = 19^2\)
Let a = 2y-5, b = 19

\(a^2 - b^2= (a+b)(a-b)\)
\(= (2y-5+19)(2y-5-19)\)
\(= (2y+14)(2y-24)\)

Solve for 2 equations
\(2y + 14 = 0\)
\(2y = -14\)
\(y = -7\)

\(2y -24 = 0\)
\(2y = 24\)
\(y = 12\)

If y = -7, then y + 2 = -7 + 2 = -5
-5 matches answer choice E
If y = 12, then y + 2 = 12 + 2 = 14
None of the answer choices has 14 as an option

Therefore, answer is E