Solving 2(x - 5)² = 32 by dividing and taking square roots

[Casio1]

Hi everyone(Wink)

I have an equation which looks like quadratic to me.

2(x - 5)² = 32

Can I divide both sides by 2?

(x - 5)² = 16

Can I take the square root?

x - 5 = + or - 4

if x = 5 plus 4 = 9

if x = 5 - 4 = 1

Therefore my roots would be;

x = 9 or x = 1

Is this method acceptable and the correct way to find the values of x. I know it works out OK but am wondering about the way I have done it?

Thanks

 

[Jameson]

Hi Casio!

(Yes) Well done. That's exactly how you should do this problem every step of the way.

 

[Fantini]

Yes, that is a perfectly valid procedure. All of your steps are correct. (Nod)

 

[MarkFL]

After dividing by 2, we may also arrange as the difference of squares:

(x - 5)² - 4² = 0

((x - 5) + 4)((x - 5) - 4) = 0

(x - 1)(x - 9) = 0

x = 1, 9