Only I understand the right way to give a hint for this.

[lookagain]

Originating in this thread:

You've been provided two hints.

And the hints were either misleading/incomplete or wrong, so they are
disadvantages to the student.

It was wrong for whomever to have deleted my posts. I corrected the hints, and
the person who deleted it must not understand how the hints are wrong, too.

Also, taking each side to ^(1/2):
x - 7 = (-4)^(1/2)

That is wrong.

(-4)^(1/2) = 2i

But (x - 7)^2 = -4 is a quadratic equation with distinct complex solutions.

 

[pka]

And the hints were either misleading/incomplete or wrong, so they are
disadvantages to the student. REALLY?
(-4)^(1/2) = 2i NO!

\(\displaystyle (x-7)^2 =- 4\) for x

\(\displaystyle \begin{align*}(x-7)&=-2\bf{i}\\x&=7-2\bf{i}\end{align*} \) OR \(\displaystyle \begin{align*}(x-7)&=2\bf{i}\\x&=7+2\bf{i}\end{align*}\)

 

[Deleted member 4993]

Originating in this thread:



And the hints were either misleading/incomplete or wrong, so they are
disadvantages to the student.

It was wrong for whomever to have deleted my posts. I corrected the hints, and
the person who deleted it must not understand how the hints are wrong, too.



That is wrong.

(-4)^(1/2) = 2i

But (x - 7)^2 = -4 is a quadratic equation with distinct complex solutions.

LookAgain - I don't understand what you are fussing about!!!

My hint was:

-4 = (2i)²

Then the original problem was:

(x-7)² = -4

(x-7)² = (2i)²

(x-7)² - (2i)² = 0

(x-7+2i)(x-7-2i) =0

x = 7 - 2i or x = 7 + 2i

Now tell me again why the hint [(x-7)² = -4] was wrong/misleading. Hints by definition should be incomplete - yes - because we expect the student to complete it.

Similarly Denis's hint was NOT wrong - continuation of the problem (as pka showed) would be the second solution.

If OP came back with WORK showing only one solution - and we did not guide him/her to the second solution - after showing incomplete work (not hints) - that would have been wrong.

Before jumping up and down - pointing fingers - read and think....

 

[lookagain]

Now tell me again why the hint [(x-7)² = -4] \(\displaystyle \ \ \ \ \)That's not a hint. It's the original problem.

was wrong/misleading.

Similarly Denis's hint was NOT wrong - continuation of the problem (as pka showed) would be the second solution.

Wrong. You and pka don't respectively know what you're talking about. Denis's hint is wrong math.
Denis doesn't get a pass for writing something incomplete. He wrote a step, which has to be fully correct.
Denis didn't even know then and/or possibly still doesn't know his step is wrong.


Note:

(-4)^(1/2) = \(\displaystyle \ \sqrt{-4 \ } \ = \ 2i.\)

-(-4)^(1/2) = \(\displaystyle \ -\sqrt{-4 \ } \ = \ -2i.\)


- -- - - - - - - - - - - - --- -- - - - - -- - - - - - - -


(x - 7)^2 = -4

\(\displaystyle x - 7 \ = \ \pm(-4)\)^(1/2)

\(\displaystyle x - 7 \ = \ \pm\sqrt{-4 \ }\)

\(\displaystyle x - 7 \ = \ \pm2i\)

\(\displaystyle x \ = \ 7 \pm2i\)

\(\displaystyle x \ = \ 7 - 2i \ \ \ or \ \ \ x \ = \ 7 + 2i\)

 

[Deleted member 4993]

Wrong. You and pka don't respectively know what you're talking about. Denis's hint is wrong math.
Denis doesn't get a pass for writing something incomplete. He wrote a step, which has to be fully correct.
Denis didn't even know then and/or possibly still doesn't know his step is wrong.


Note:

(-4)^(1/2) = \(\displaystyle \ \sqrt{-4 \ } \ = \ 2i.\)

-(-4)^(1/2) = \(\displaystyle \ -\sqrt{-4 \ } \ = \ -2i.\)


- -- - - - - - - - - - - - --- -- - - - - -- - - - - - - -


(x - 7)^2 = -4

\(\displaystyle x - 7 \ = \ \pm(-4)\)^(1/2)

\(\displaystyle x - 7 \ = \ \pm\sqrt{-4 \ }\)

\(\displaystyle x - 7 \ = \ \pm2i\)

\(\displaystyle x \ = \ 7 \pm2i\)

\(\displaystyle x \ = \ 7 - 2i \ \ \ or \ \ \ x \ = \ 7 + 2i\)

Again - read and think and then type..... and read it again .....