Question

Solve for x : 6a²x² - 7abx - 3b² = 0 , a is not equal to zero , by method of completing the square

Answer 1

Given,

$6a^2{x}^2-7abx-3b^2=0;a\ne 0$

$\Rightarrow x^2-\frac{7abx}{6a^2}-\frac{3b^2}{6a^2}=0$

$\Rightarrow x^2-\frac{7b}{6a}x-\frac{b^2}{2a^2}=0$

$\Rightarrow x^2-\frac{7b}{6a}x+\frac{49b^2}{144a^2}-\frac{49b^2}{144a^2}-\frac{b^2}{2a^2}=0$

$\Rightarrow {(x-\frac{7b}{12a})}^2=\frac{49b^2}{144a^2}+\frac{b^2}{2a^2}$

$\Rightarrow (x-\frac{7b}{12a})=\pm \frac{11b}{12a}$

$\Rightarrow x=\frac{11b}{12a}+\frac{7b}{12a}$ or $x=-\frac{11b}{12a}+\frac{7b}{12a}$

$\Rightarrow x=\frac{3b}{2a}orx=-\frac{b}{3a}$