Question
Solve the following quadratic equation by completing the square method.
$5 x^2=4 x+7=0$
$5 x^2=4 x+7=0$
✓
Answer
$5 x^2-4 x-7=0 $
$ \Rightarrow x^2-\frac{4}{5} x-\frac{7}{5}=0 $
$ \left.\Rightarrow x^2-\frac{4}{5} x+\frac{4}{25}=\frac{7}{5}+\frac{4}{25} \text { (Adding and Subtracting } \frac{4}{25}\right) $
$ \Rightarrow\left(x+\frac{2}{5}\right)^2=\frac{35+4}{25} $
$ \Rightarrow\left(x+\frac{2}{5}\right)^2=\frac{39}{25} $
$ \Rightarrow x+\frac{2}{5}=\sqrt{\frac{39}{25}}$
$ \Rightarrow x+\frac{2}{5}= \pm \frac{\sqrt{39}}{5} $
$ x=\frac{\sqrt{39}}{5}-\frac{2}{5} \text { or } x=-\frac{\sqrt{39}}{5}-\frac{2}{5} $
$x=\frac{\sqrt{39}}{5}-2 { or } x=\frac{-\sqrt{39}-2}{5}$
$ \Rightarrow x^2-\frac{4}{5} x-\frac{7}{5}=0 $
$ \left.\Rightarrow x^2-\frac{4}{5} x+\frac{4}{25}=\frac{7}{5}+\frac{4}{25} \text { (Adding and Subtracting } \frac{4}{25}\right) $
$ \Rightarrow\left(x+\frac{2}{5}\right)^2=\frac{35+4}{25} $
$ \Rightarrow\left(x+\frac{2}{5}\right)^2=\frac{39}{25} $
$ \Rightarrow x+\frac{2}{5}=\sqrt{\frac{39}{25}}$
$ \Rightarrow x+\frac{2}{5}= \pm \frac{\sqrt{39}}{5} $
$ x=\frac{\sqrt{39}}{5}-\frac{2}{5} \text { or } x=-\frac{\sqrt{39}}{5}-\frac{2}{5} $
$x=\frac{\sqrt{39}}{5}-2 { or } x=\frac{-\sqrt{39}-2}{5}$
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