Question

Solve $13x^2-49x+30=0$

Answer 1

$13x^2-49x+30=0$

$=13(x^2-\frac{49}{13}x+\frac{30}{13})=0$ by dividing the equation by $13$

$\Rightarrow x^2-2\times \frac{49}{2\times 13}+{\left(\frac{49}{26}\right)}^2-{\left(\frac{49}{26}\right)}^2+\frac{30}{13}=0$

$\Rightarrow {(x-\frac{49}{26})}^2={\left(\frac{49}{26}\right)}^2-\frac{30}{13}$

$\Rightarrow {(x-\frac{49}{26})}^2=\frac{2401}{676}-\frac{30}{13}$

$\Rightarrow {(x-\frac{49}{26})}^2=\frac{31213-20280}{676\times 13}=\frac{10933}{676\times 13}$

$x-\frac{49}{26}=\pm \sqrt{\frac{10933}{676\times 13}}=\pm \frac{1}{26}\sqrt{\frac{10933}{13}}=\pm \frac{\sqrt{841}}{26}=\pm \frac{29}{26}$

$\Rightarrow x-\frac{49}{26}=\pm \frac{29}{26}$

$\Rightarrow x=\pm \frac{29}{26}+\frac{49}{26}$

$\Rightarrow x=\frac{49+29}{26}=\frac{78}{26}=3$ and $x=\frac{49-29}{26}=\frac{10}{13}$

$\therefore x=\frac{10}{13},3$