# How do I solve x^2 + 12x = -27 by completing the square?

Aug 29, 2014

${x}^{2} + 12 x = - 27$

Take the co-efficient of the middle $x$ term and half it

$\frac{12}{2} = 6$

Square that number and add and subtract it from the equation
This gives the perfect square component.

${6}^{2} = 36$

${x}^{2} + 12 x + \left(36\right) - \left(36\right) = - 27$

Then factorise it, the first three terms form a perfect square

${\left(x + 6\right)}^{2} - 36 = - 27$

Simplify left over numbers

${\left(x + 6\right)}^{2} = 9$

Now we solve for $x$

Square root both sides to get rid of the power

$\left(x + 6\right) = \pm 3$
$x = \pm 3 - 6$
$x = 3 - 6$ or $x = - 3 - 6$
$x = - 3$ or $x = - 9$