Question
Solve the following quadratic equation.
$x^2-\frac{3 x}{10}-\frac{1}{10}=0$
$x^2-\frac{3 x}{10}-\frac{1}{10}=0$
✓
Answer
$10 x ^2-3 x -1=0 $
$ \Rightarrow 10 x ^2-3 x -1=0 \text { compare with } ax ^2+ bx + c =0 $
$ \Rightarrow a =10, b=-3 \text { and } c =-1$
$ \therefore b ^2-4 ac =-3^2-4(10)(-1) $
$ =9+40$
$=49 $
$ x =\frac{- b \pm \sqrt{ b ^2-4 a c}}{2 a } $
$ \Rightarrow x =\frac{3 \pm \sqrt{49}}{2 \times 10} $
$ \Rightarrow x =\frac{3 \pm 7}{20} $
$ \Rightarrow x =\frac{3+7}{20} \text { or } x =\frac{3-7}{20} $
$ \Rightarrow x =\frac{10}{20} \text { or } x =\frac{-4}{20} $
$ \Rightarrow x =\frac{1}{2} \text { or } x =-\frac{1}{5}$
$ \Rightarrow 10 x ^2-3 x -1=0 \text { compare with } ax ^2+ bx + c =0 $
$ \Rightarrow a =10, b=-3 \text { and } c =-1$
$ \therefore b ^2-4 ac =-3^2-4(10)(-1) $
$ =9+40$
$=49 $
$ x =\frac{- b \pm \sqrt{ b ^2-4 a c}}{2 a } $
$ \Rightarrow x =\frac{3 \pm \sqrt{49}}{2 \times 10} $
$ \Rightarrow x =\frac{3 \pm 7}{20} $
$ \Rightarrow x =\frac{3+7}{20} \text { or } x =\frac{3-7}{20} $
$ \Rightarrow x =\frac{10}{20} \text { or } x =\frac{-4}{20} $
$ \Rightarrow x =\frac{1}{2} \text { or } x =-\frac{1}{5}$
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