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
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
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
$\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}$
$\displaystyle =\frac{-188\pm\sqrt{188^2-4(252)(-225)}}{2\cdot252}$
$\displaystyle =\frac{-188\pm\sqrt{188^2+4\cdot252\cdot225}}{504}$
$\displaystyle =\frac{-188\pm\sqrt{35\,344+226\,800}}{504}$
$\displaystyle =\frac{-188\pm\sqrt{262\,144}}{504}$
$\displaystyle =\frac{-188\pm512}{504}$
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.