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

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Answer 1 · 2014-08-29T12:39:14

$x^2+12x=-27$

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

$12/2 =6$

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

$6^2=36$

$x^2+12x+(36)-(36)=-27$

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

$(x+6)^2-36=-27$

Simplify left over numbers

$(x+6)^2=9$

Now we solve for $x$

Square root both sides to get rid of the power

$(x+6)=+-3$
$x=+-3-6$
$x=3-6$ or $x=-3-6$
$x=-3$ or $x=-9$

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