please explain the '1/12': (1/2x)^2 – 5(1/2x) – 6 = 0

[Jodene222]

please explain the '1/12': (1/2x)^2 – 5(1/2x) – 6 = 0

(1/2x)^2 – 5(1/2x) – 6 = 0

Let z = ½ x

Then,
z^2 – 5z – 6 = 0

(z + 1) (z – 6) = 0

z = -1 z = 6

If z = 1/2x
then x = -1/2, 1/12

MY QUESTION IS:
I understand everything except the 1/12. I want to multiply each side by 2 so the ½ will cross out and 6 x 2 is 12. Why is the answer 1/12??? It only seems logical to me that x has to be 12 because ½ of a number (x) equal to 6 is 12. Please explain the real answers are the reciprocal of my answers. WHY?

 

[stapel]

Is the equation either of the following?

. . . . .\(\displaystyle \left(\frac{1}{2x}\right)^2\, - \, 5\left(\frac{1}{2x}\right)\, -\, 6\, =\, 0\)

. . . . .\(\displaystyle \left(\frac{1}{2}x\right)^2\, - \, 5\left(\frac{1}{2}x\right)\, -\, 6\, =\, 0\)

Or something else? :?:

Thank you!

Eliz.

 

[masters]

Re: please explain the '1/12': (1/2x)^2 – 5(1/2x) – 6 = 0

It all depends on where the x is in your equation. If it is in the denominator, then your solutions are correct. However, if x is in the numerator in your equation, then the solutions are the reciprocals of what you found. Check your original equation to be sure where the variable is placed.