Question

Find the roots of the following equation $4x^2+4bx-(a^2-b^2)=0$ by the method of completing the square.

Answer 1

$4x^2+4bx-(a^2-b^2)=0$

$x^2+bx-\left(\frac{a^2-b^2}{4}\right)=0$

$x^2+2\left(\frac{b}{2}\right)x=\frac{a^2-b^2}{4}$

$x^2+2\left(\frac{b}{2}\right)x+(\frac{b}{2}{)}^2=\frac{a^2-b^2}{4}+(\frac{b}{2}{)}^2$

$(x+\frac{b}{2}{)}^2=\frac{a^2}{4}$

$x+\frac{b}{2}=\pm \frac{a}{2}$

$x=-\frac{b}{2}\pm \frac{a}{2}$