I'm hoping for link to some resource which can explain why the following is true.

$$x^2 + 104x - 896 = 0$$

Using the quadratic formula we pull a = 1, b = 104, c = 896. Putting that into the formula for the discriminant we get $104^2 - 4.1.896$ which is 10816 - 3584 = 7232.

$$-104 \pm \sqrt{7232} \over 2$$

This simplfies to $-72 \pm 4 \sqrt{113}$.

The problem I have is I have not found anything which explains why if you plug x = 8 into the equation it also balances out. What I have found out infers x = 8 being an answer to the equation but not a factor and so not a solution but I don't really get the point.

Any links that explain the distinction would help. I have an infinite number of these equations which I'm looking for integer answers to so if said link also pointed out how you can obtain the integer answers like the 8 in this case instead of the irrational provided by the quadratic formula that would be great.

• Scrap that 896 is correct. 8^2 is 64. 8*104 = 832 so it is 896. Checking the quadratic to see if I made a mistake working that out instead. I have other examples anyway. Dec 9, 2013 at 11:12
• @Jp McCarthy sorry editied comment instead of answering again. I've double checked and I had an error alright but it was in the discriminant. Have changed to correct value. 8 still works but the value provide by quadratic formula had the typo. I'll write out all values so you can double check and point out the error if existant. Dec 9, 2013 at 11:27
• @Jp McCarthy have written out all the calculations please spot the error for me please. If it is only down to a bad calculation on my part rather than an lack of understanding on roots versus answers which work when plugged in I'll be happy. Dec 9, 2013 at 11:42

The quadratic formula is $$x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}.$$ Thus in your problem, $$x = \frac{-104\pm\sqrt{104^2 - 4(-896)}}{2} =\frac{-104 \pm\sqrt{14400}}{2} = \frac{-104 \pm 120}{2}.$$ This gives $x = 8$ or $-112$.

It seems the problem in your computation was you forgot the negative on $896$ when you plugged it into the quadratic formula.

• lols thanks. I must have done that multiple times. Some of the stuff I read earlier tonight wasn't very clear was (it was saying something about plugging values in for specific terms which made me think there was a lack of understanding on my part instead of just bad sums. Dec 9, 2013 at 12:02

I cannot comment, but you are obviously mistaken in your calculation. Your quadratic formula that is. Here, WA does not make mistakes

EDIT: $$\frac{-104\pm\sqrt{104^2+4\cdot 896}}{2}\\ =\frac{-104\pm\sqrt{14400}}{2}=-52\pm60$$

• ndh I have read quite a bit trying to find the answer. Please check my values which I have written out now in full and point to the mistake. I've tripled checked this example and I have plenty of others. As I said it isn't that the quadratic formula doesn't give the correct value, all the values work out if you use them for x. Dec 9, 2013 at 11:38
• I added the correct use of the quadratic formula. There are only two answers here Dec 9, 2013 at 11:50
• He made two mistakes: (1) is that '-104/2' is '-52' not '-72' (2) is that "1042−4.1.896" ("." is '*') should be '1042+4*896' Dec 9, 2013 at 12:05

obviously 8 is one of the solutions with no doubts at all.