Question

What constant must be added or subtracted to solve the equation $5x^2-\sqrt{2}x+3=0$ by the method of completing the square?

Answer 1

$5x^2-\sqrt{2}x+3=0$
We can convert it in the from of
$(a-b{)}^2=a^2-2ab+b^2$
Comparing,
$a^2=5\Rightarrow a=\sqrt{5}$
$2ab=\sqrt{2}$
$\Rightarrow b=\frac{\sqrt{2}}{2a}=\frac{1}{\sqrt{2}\times \sqrt{5}}=\frac{1}{\sqrt{10}}$
$Thus,b^2={\left(\frac{1}{\sqrt{10}}\right)}^2=\frac{1}{10}$
We need to subtract $(3-\frac{1}{10})=\frac{29}{10}=2.9$
To get perfect square