# Thread: sing the quadratic formula with large numbers

1. ## using the quadratic formula with large numbers

solving this using quadratic formula

252x^2 + 188x - 225 = 0

i got (-188± √188^2 - 4*252*-225)/504

but even when I compute it I must be making a mistake because I do not get the right answer

2. ## Re: sing the quadratic formula with large numbers

i keep getting 379.5 and 519.753968 as the roots, which according to my text is wrong

3. ## Re: sing the quadratic formula with large numbers

i found this online (from a quadratic calculator)

−188±512* square root 1
----------------------------
504

how does one know to multiply by the square root of one?

I thought the formula called for the square root of b^2-4ac, and if b^2-4ac comes out to 262114 then it's root is 512, where does the 'times the square root of one' come in?

MH

4. ## Re: using the quadratic formula with large numbers

Originally Posted by kingsolomonsgrave
252x^2 + 188x - 225 = 0
$\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$\displaystyle =\frac{-188\pm\sqrt{188^2-4(252)(-225)}}{2\cdot252}$

$\displaystyle =\frac{-188\pm\sqrt{188^2+4\cdot252\cdot225}}{504}$

$\displaystyle =\frac{-188\pm\sqrt{35\,344+226\,800}}{504}$

$\displaystyle =\frac{-188\pm\sqrt{262\,144}}{504}$

$\displaystyle =\frac{-188\pm512}{504}$

So

$\displaystyle x = \frac{-188+512}{504}=\frac{324}{504}=\frac9{14}$

or

$\displaystyle x = \frac{-188-512}{504}=-\frac{700}{504}=-\frac{25}{18}$

You can make the arithmetic a little bit easier by doing some factoring, but the above is what you should get through direct calculation.

5. ## Re: sing the quadratic formula with large numbers

Originally Posted by kingsolomonsgrave
i found this online (from a quadratic calculator)
...
how does one know to multiply by the square root of one?
$\displaystyle 512\cdot\sqrt1=512\cdot1=512$. The format it gave you was probably a peculiarity of that specific calculator. I would guess that it gives all answers in a radical form.