Is This the Right Way to Solve a Quadratic Equation?

[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

 

[CellCoree]

for sharing your equation with us. It does indeed appear to be a quadratic problem. Your method of dividing both sides by 2 and taking the square root is a valid way to solve for the values of x. However, in order to ensure accuracy, it is always a good idea to check your solutions by plugging them back into the original equation. In this case, both x = 9 and x = 1 satisfy the equation, so your method is correct.

Additionally, there are other methods for solving quadratic equations, such as factoring or using the quadratic formula. It is always good to be familiar with multiple methods and choose the one that works best for a particular problem. Keep up the good work in solving quadratic problems!