Question
Solve the following quadratic equation using formula method only :
$16x^2 = 24x + 1$
$16x^2 = 24x + 1$
✓
Answer
$16 x^2=24 x+1 $
$ 16 x^2-24 x-1=0 $
$ x^2-\frac{3}{2} x-\frac{1}{16}=0$
$ a=1 ; b=-\frac{3}{2} ; c=-\frac{1}{16} $
$ D=b^2-4 a c$
$=\left(-\frac{3}{2}\right)^2-4(1)\left(-\frac{1}{16}\right) $
$ =\frac{9}{4}+\frac{1}{4} \\ =\frac{10}{4}$
$x =\frac{- b \pm \sqrt{ b ^2-4 ac }}{2 a}$
$x =\frac{-\left(-\frac{3}{2}\right) \pm \sqrt{\frac{10}{4}}}{2 \times 1}$
$ x =\frac{3+\sqrt{10}}{4}, x=\frac{3-\sqrt{10}}{4}$
$ 16 x^2-24 x-1=0 $
$ x^2-\frac{3}{2} x-\frac{1}{16}=0$
$ a=1 ; b=-\frac{3}{2} ; c=-\frac{1}{16} $
$ D=b^2-4 a c$
$=\left(-\frac{3}{2}\right)^2-4(1)\left(-\frac{1}{16}\right) $
$ =\frac{9}{4}+\frac{1}{4} \\ =\frac{10}{4}$
$x =\frac{- b \pm \sqrt{ b ^2-4 ac }}{2 a}$
$x =\frac{-\left(-\frac{3}{2}\right) \pm \sqrt{\frac{10}{4}}}{2 \times 1}$
$ x =\frac{3+\sqrt{10}}{4}, x=\frac{3-\sqrt{10}}{4}$
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