# How do you solve using the completing the square method x^2 + 10x + 16 = 0?

Feb 26, 2016

$x = - 2$ and $x = - 8$

#### Explanation:

To solve the equation ${x}^{2} + 10 x + 16 = 0$ using the completing square method, as coefficient of ${x}^{2}$ is $1$ and independent term $16$ positive, we have to identify factors of $16$ whose sum is $10$, coefficient of $x$ term.

These are $2$ and $8$ and hence we should split the equation as follows:

${x}^{2} + 2 x + 8 x + 16 = 0$ or $x \left(x + 2\right) + 8 \left(x + 2\right) = 0$ i.e.

$\left(x + 2\right) \left(x + 8\right) = 0$.

Hence either $x + 2 = 0$ i.e. $x = - 2$ or

$x + 8 = 0$ i.e. $x = - 8$

[In general if equation is in form $a {x}^{2} + b x + c = 0$, one should identify two factors whose product is $a \cdot c$ and sum is $b$.]