# How do you solve using the completing the square method x^2 +8x+14=0 ?

Jun 16, 2016

$x = - 2.586 \text{ or } - 5.414$

#### Explanation:

NOte that when you square a binomial there is always a particular pattern for the answer.

${\left(x - 3\right)}^{2} = {x}^{2} - 6 x + 9 \text{ } \left(a {x}^{2} + b x + c\right)$
As long as $a = 1$, then there is always the same relationship between b and c.
${\text{(half of b)}}^{2}$gives $c . \text{ }$ check (-6 ÷ 2)^2 = (-3)^2 = 9

In ${x}^{2} + 8 x + 14 = 0$ we would like the left side to be written as

${\text{(binomial)}}^{2}$

1. Move the constant to the right side.
${x}^{2} + 8 x \text{ } = - 14$

2. Add the missing term to both sides ${\left(\frac{b}{2}\right)}^{2}$
${x}^{2} \textcolor{b l u e}{+} 8 x + \textcolor{red}{16} = - 14 + \textcolor{red}{16}$

This is the part that is COMPLETING THE SQUARE.
(Add in what is missing to form a perfect square)

1. The left side is the answer to the square of a binomial;
${\left(x \textcolor{b l u e}{+} 4\right)}^{2} = 2$

2. Find the square root of each side.
$x + 4 = \pm \sqrt{2}$

3. Solve for $x$ twice, once with $+ \sqrt{2}$, once with $- \sqrt{2}$
$x = + \sqrt{2} - 4 \text{ or } x = - \sqrt{2} - 4$7
$x = - 2.586 \text{ or } - 5.414$