Question

Which constant should be added and subtracted to solve the quadratic equation $4x^2-\sqrt{3}x-5=0$ by the method of completing the square?

• A. $\frac{9}{10}$
• B. $\frac{3}{16}$
• C. $\frac{3}{4}$
• D. $\frac{\sqrt{3}}{4}$

Answer 1

Answer: (B)

$\frac{3}{16}$

We have,
$4x^2-\sqrt{3}x-5=0$
Divide whole equation by $4$,
$\therefore x^2-\frac{\sqrt{3}}{4}x-\frac{5}{4}=0$
$\therefore {(x-\frac{\sqrt{3}}{8})}^2-\frac{5}{4}=\frac{3}{64}$
$\Rightarrow 4{(x-\frac{\sqrt{3}}{8})}^2-5-\frac{3}{16}=0$
$\therefore \frac{3}{16}$ must be added to make $4x^2-\sqrt{3}x-5=0$ a complete square