Solve this question? (grade 10) find "a" so that the distance between points (-2,-3) and (-3, a) is equal to 5

can you please simply explain how to solve this? I though it would be 5= √(-3 -(-2))² + (a-(-3))² but

apparently I'm wrong. The answer's supposed to be either a= -3 + 2√6 or a= -3- 2√6

anyways, I'd appreciate it if you could explain it in simple terms please
thanks!

Your orginal solution is right, you just need to solve for the unknown "a".
First expand your orginal solution and square both sides and get a^2 + 6a +10 = 25
which equals a^2 + 6a - 15 which has the form AX^2 + BX +C where A, B, and C are coefficients.

now use
X = (-B + or - sqrt (B^2 - 4AC)) / 2A

And you will get their answers.

√[ (-3 -(-2))² + (a-(-3))² ] = 5

√[ (-3 -(-2))² + (a-(-3))² ] ² = 5 ²

√[ (- 1)² + (a + 3)² ] ² = 5 ²

√[ 1 + (a + 3)² ] ² = 5 ²

1 + (a + 3)² = 25

(a + 3)² = 24

√(a + 3)² = + - √24 = + - 2√6

a + 3 = + - 2√6

a = - 3 + - 2√6.............ANSWERS

Mathcerely, Robert Jones "Teacher/Tutor of Fine Students"
Moved Florida to France June 2011 but still tutor world-wide (USA , UK ,
France , Checz Republic ...) free using Skype. If you need me to explain
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********* A PRESENT FOR YOU
Ask someone to write a number, say a five-digit number.
(Can be a 2-digit.....3-digit.....4-digit....ect..…
Suppose the number written is
57836
Now, without showing the asker, you write a number on
a sheet of paper and keep it folded. You have to write the
number by subtracting 2 from the above number and
adding 2 in front which will be....
257834
Next, ask the person to write another five-digit number
below his original number. Suppose he writes 37589.
So you now have...
57836
37589
Now you write a five-digit number below it in such a