# How do you solve using the completing the square method  x^2+8x=9?

Feb 28, 2016

$x = 1$ or $x = 9$
(see below for method of completing the square).

#### Explanation:

A general squared binomial has the relation:
$\textcolor{w h i t e}{\text{XXX}} {\left(a + b\right)}^{2} = {a}^{2} + 2 a b + {b}^{2}$

If ${x}^{2} + 8 x$ are the first two terms of an expanded squared binomial
then $a = 1$ and $b = 4$
and the third term needed to complete the square would be ${b}^{2} = 16$.

If we add $16$ to the left side to complete the square there
we will need to add $16$ to the right side to maintain the equality.
$\textcolor{w h i t e}{\text{XXX}} {x}^{2} + 8 x + 16 = 9 + 16$

Re-writing the left side as a squared binomial and simplifying the right side:
$\textcolor{w h i t e}{\text{XXX}} {\left(x + 4\right)}^{2} = 25$

If we take the square root of both sides:
$\textcolor{w h i t e}{\text{XXX}} \left(x + 4\right) = \pm 5$

which implies:
either $x = 1$ or $x = - 9$