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

  • Thread starter Thread starter Casio1
  • Start date Start date
  • Tags Tags
    Quadratic
AI Thread Summary
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.
Casio1
Messages
86
Reaction score
0
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
 
Mathematics news on Phys.org
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
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.

Similar threads

Back
Top