MHB Is This the Right Way to Solve a Quadratic Equation?

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The discussion centers on solving the quadratic equation 2(x - 5)² = 32. The method presented involves dividing both sides by 2, simplifying to (x - 5)² = 16, and then taking the square root to find x = 9 or x = 1. Participants confirm that this approach is valid and correctly executed. An alternative method using the difference of squares is also suggested, leading to the same roots. Overall, the steps taken to solve the equation are deemed acceptable and accurate.
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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
 
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Hi Casio!

(Yes) Well done. That's exactly how you should do this problem every step of the way.
 
Yes, that is a perfectly valid procedure. All of your steps are correct. (Nod)
 
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
 

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