# How do you solve using the completing the square method x^2+6x+4=0?

Mar 17, 2017

#### Answer:

$x = - 0.76393202 \mathmr{and} x = - 5.23606797$

#### Explanation:

$\textcolor{red}{C o m m e n c i n g}$ $\textcolor{red}{c o m p l e t i n g}$ $\textcolor{red}{t h e}$ $\textcolor{red}{s q u a r e}$ $\textcolor{red}{m e t h o d}$ $\textcolor{red}{n o w ,}$

1) Know the formula for the perfect quadratic square, which is,

${\left(a x \pm b\right)}^{2} = a {x}^{2} \pm 2 a b x + {b}^{2}$

2) Figure out your $a \mathmr{and} b$ values,

$a =$ coefficient of ${x}^{2}$, which is $1$.
$\textcolor{red}{b = \frac{6}{2 \left(1\right)} = 3}$

3) Move the $4$ over to the right hand side,

${x}^{2} + 6 x = - 4$

4) Add $\textcolor{red}{{b}^{2}}$ on both sides of the equation, giving you an overall net of 0, hence not affecting the result of the equation,

${x}^{2} + 6 x + \textcolor{red}{{3}^{2}} = - 4 + \textcolor{red}{{3}^{2}}$
${\left(x + 3\right)}^{2} = 5$

5) Square root both sides,

$x + 3 = \pm \sqrt{5}$

6) Move the $3$ over to the right side,

$x = \pm \sqrt{5} - 3$

7) Calculate the two values of $x$,

$x = - 0.76393202 \mathmr{and} x = - 5.23606797$