Find the roots of the following quadratic equations (if they exist) by the method of completing the square.

$x^2 - 8x + 18 = 0$

Given:

Given quadratic equation is $x^2 - 8x + 18 = 0$.

To do:

We have to find the roots of the given quadratic equation.

Solution:

$x^2 - 8x + 18 = 0$

$x^2 + 2\times 4x = -18$  

Adding $(4)^2$ on both sides completes the square. Therefore,

$x^2 + 2\times 4 x + (4)^2 = -18+(4)^2$

$(x+4)^2=-18+16$      (Since $(a+b)^2=a^2+2ab+b^2$)

$(x+4)^2=-2$

$x+4=\pm \sqrt{-2}$     (Taking square root on both sides)

$x=\sqrt{-2}-4$ or $x=-\sqrt{-2}-4$

Therefore, no real roots exist for the given quadratic equation. 

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

24 Views

Kickstart Your Career

Get certified by completing the course

Get Started