Question

Find the roots of the following quadratic equations, if they exist, by the method the square:
$5x^2-7x-6=0$

Answer 1

$5x^2-7x-6=0$

$(\sqrt{5x}{)}^2-2\times \frac{7}{2\sqrt{5}}\times \sqrt{5x}-6=0$

$(\sqrt{5x}{)}^2-7x+\frac{49}{20}-\frac{49}{20}-6=0$

$(\sqrt{5x}-\frac{7}{2\sqrt{5}}{)}^2-\frac{169}{20}=0$

$(\sqrt{5x}-\frac{7}{2\sqrt{5}}{)}^2-(\frac{13}{2\sqrt{5}}{)}^2=0$

$(\sqrt{5x}-\frac{7}{2\sqrt{5}}-\frac{13}{2\sqrt{5}})(\sqrt{5x}-\frac{7}{2\sqrt{5}}{)}^2+\frac{13}{2\sqrt{5}}=0$

$\sqrt{5x}-\frac{20}{2\sqrt{5}}=0$ or $\sqrt{5x}=\frac{-6}{2\sqrt{5}}$

[x=2] $[x=\frac{-3}{5}]$

$\therefore$ $[x=2,\frac{-3}{5}]$.