### Home > INT2 > Chapter 12 > Lesson 12.2.1 > Problem12-70

12-70.

$x^2 - 6x + 11 = 0$

Use the example below.

Example: Solve $x^2+5x+4=0$ by completing the square.

Solution: This method works most efficiently when the coefficient of $x^2$ is $1$.
Rewrite the equation as $x^2+5x=-4$. Rewrite the left side as an incomplete square:

 $2.5$$+$$x$ $2.5x$ $=-4$ $x^2$ $2.5x$ $x+2.5$

Complete the square and rewrite as
$(x+2.5)^2-6.25=-4$ or $(x+2.5)^2=2.25$

Take the square root of both sides, $x+2.5=\underline{+}1.5$. Solving for $x$ reveals that
$x=-1$ or $x=-4$.