1. ## Why not solve the quadratic this way?

I have (289^2)+(-1666)+(2401)=(x^2-5)

then I, (289^2)+((-1666)+(2401))=(x^2-5)

then I have, (289^2)+(735)=(x^2-5) then subtract (x^2) and add 5 to both sides.

So now I have (288x^2)+740=0

So then, subtract 740 from both parts to get (288x^2)=-740

Finally do this -740/288=x^2, so x=(-2.5)^(1/2) which is imaginary. But the equation has only real solutions. But it looks like the answer was derived using all correct principles...?

2. Originally Posted by bournouli
I have (289^2)+(-1666)+(2401)=(x^2-5)

then I, (289^2)+((-1666)+(2401))=(x^2-5)

then I have, (289^2)+(735)=(x^2-5) then subtract (x^2) and add 5 to both sides.

So now I have (288x^2)+740=0

So then, subtract 740 from both parts to get (288x^2)=-740

Finally do this -740/288=x^2, so x=(-2.5)^(1/2) which is imaginary. But the equation has only real solutions. But it looks like the answer was derived using all correct principles...?
Why are there so many PARENTHESIS?!?!
Is the original equation 289^2 - 1666 + 2401 = x^2 - 5 ???

3. Maybe because 289^2 doesn't have an x^2 term, so they are not like terms and can not be added/subtracted...

4. Originally Posted by Prove It
Maybe because 289^2 doesn't have an x^2 term, so they are not like terms and can not be added/subtracted...
Sorry it was (289x^2).

5. Originally Posted by bournouli
Sorry it was (289x^2).
If and only if the original equation was:

289x^2 - 1666x + 2401 = x^2 - 5

then you'll get the solutions x = 3 or x = 401/144

... but my crystal sphere is a little bit dusty