How do you solve x^2+9x+20.25=0 by completing the square?

Dec 18, 2016

$x = - \frac{9}{2} = - 4.5$

Explanation:

The left hand side is already a perfect square trinomial:

${\left(x + \frac{9}{2}\right)}^{2} = {x}^{2} + 9 x + \frac{81}{4} = {x}^{2} + 9 x + 20.25$

So the given equation is equivalent to:

${\left(x + \frac{9}{2}\right)}^{2} = 0$

Hence:

$x + \frac{9}{2} = 0$

Hence:

$x = - \frac{9}{2}$