Question

Solve the following quadratic equation by completing the square method.
$5x^2=4x+7$

Answer 1

$5x^2=4x+7$

$5x^2-4x=7$

$x^2-\frac{4}{5}x=\frac{7}{5}$

$x^2-\frac{4}{5}x+\frac{4}{25}=\frac{7}{5}+\frac{4}{25}$

$x^2-2\left(\frac{2}{5}\right)x+{\left(\frac{2}{5}\right)}^2=\frac{39}{25}$

${(x-\frac{2}{5})}^2=\frac{39}{25}$

$x-\frac{2}{5}=\pm \sqrt{\frac{39}{25}}$

$x=\frac{2}{5}\pm \frac{\sqrt{39}}{5}$

$\therefore x=\frac{2\pm \sqrt{39}}{5}$