Question

Solve each of the following equation by using the method of completing the square:
$8x^2+14x-1=0$ ?

Answer 1

Given,

$8x^2+14x-1=0$

$x^2+\left(\frac{14}{8}\right)x-1=0$

$x^2+\left(\frac{7}{4}\right)x-1=0$

add and subtract ${\left(\frac{7}{8}\right)}^2$

$x^2+\left(\frac{7}{4}\right)x-1+{\left(\frac{7}{8}\right)}^2-{\left(\frac{7}{8}\right)}^2=0$

$x^2+\left(\frac{7}{4}\right)x+{\left(\frac{7}{8}\right)}^2-1-{\left(\frac{7}{8}\right)}^2=0$

${(x+\frac{7}{8})}^2=1+\frac{49}{64}=\frac{113}{64}$

$x+\frac{7}{8}=\pm \frac{\sqrt{113}}{8}$

$\therefore x=\pm \frac{\sqrt{113}}{8}-\frac{7}{8}$